## Problem Statement**5. Use the graph of $ f'(x) $ shown and the fact that $ f(2) = 14 $ to find the value of $ f(12) $.**## Graph ExplanationThe graph presented is of the derivative $ f'(x) $ with the following characteristics:- The horizontal axis (x-axis) is labeled from $-5$ to $12$.- The vertical axis (f'(x) axis) is labeled from $-2$ to $8$.### Graph Features:1. **From $ x = -5 $ to $ x = 1 $:** - The graph is a line decreasing from the top left to bottom right, starting at $(-5, 0)$ and ending at approximately $(1, -2)$.2. **From $ x = 1 $ to $ x = 8 $:** - The graph forms a semicircle, starting from $(1, -2)$, peaking at $(5, 3)$, and descending back to $(8, 0)$.3. **From $ x = 8 $ to $ x = 12 $:** - The graph is a line increasing sharply from $ (8, 0) $ to $ (12, 8) $.## Multiple Choice Optionsa) $ \frac{9}{2} \pi + 23 $b) $ \frac{9}{2} \pi + 14 $c) $ \frac{9}{2} \pi + 28 $d) $ \frac{9}{2} \pi + 10 $e) $ \frac{9}{2} \pi + 30 $

Notice that the graph of f'(x) on 2,8 is a upper semi circle with center (5,0) and radius 3.…

Answered: 5. Use the graph of ƒ '(x) shown and…

5. Use the graph of ƒ '(x) shown and the fact that f(2) = 14 to find the value of f(12). f’(x) 8 3 -5 8. 12 a) 5T+23 9. b) T+14 9. c) -It+28 d) -T+10 2 9. e) ,7+30

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Use the given graph of y = f(x) to evaluate the following.

A: given graph of f(x)

Q: What is the maximum point on the curve = 2 + 12? − x3

A: Maxima minima problem

Q: Given a function Ax) and g(x) =-x+1, how would the graph of y = f(x) compare to the graph of y=…

A: Given, a function f(x) and g(x)=-x+1.

Q: 2(4). The given lines are the main diagonal and the graph of f (x). Graph f (x) if it exists. If…

A: We need to graph the inverse function. Firstly, check whether the function is one-one and the…

Q: Erik is throwing a ball up a long ramp. The slope of the ramp can be approximated by the equation y…

Q: If f(a)=b, then which point is on the graph of f(x)? 1. (f(a),f(b)) 2. (a, b)(a,b) 3.…

A: Given : f(a) = b

Q: 10. Differentiate each function. a) y= -3x² + 4x – 5 b) f(x)=6x¬1- 5x=2 O f(x)= 4Jx

Q: Sketch the graph of f(x) = x + 2x. Clearly label the x-intercepts and y-intercepts.

Q: Sketch the graph of the curve f(x)=3x³ - 3x + 2

Q: Assume that the number of barbeque dinners that can be sold, x can be related to the price charged,…

A: Introduction: When there are some outputs that are produced, the total cost to produce these outputs…

Q: What is the y-intercept of the function, f (x) = -3x² – 16x (-2,21) (0, 0) 0, -5

Q: 4. When Greg dives from a platform with an initial upward velocity of 12 ft/s, his height h (in…

Q: A competitive firm's profit is given by T(x,.x2) = 95(4x2 + 6x}")- 4.75x, - 15x2. %3D The stationary…

A: To find stationary point of a function fx,y, we have to find fx and fy. Then we put fx=0 and fy=0.…

Q: The graph of f(x) = where these horizontal tangents occur? 2x+3x – 120x + 20 has two horizontal…

Q: f(x)=2-\x t4| give their domain, range, -intercept, and y-intercept

Q: a) Select a point on the graph of y = -x + 2x³ + 13x² - 14x-24, where the roller coaster is going up…

A: f(x) = -x^4+2x^3+13x^2-14x-24Let's find the first derivative (f'(x)):f'(x) = -4x^3 + 6x^2 + 26 x -…

Q: Graph the function f(x) = 5(5)"

A: To graph the function

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.

Question

## Problem Statement

**5. Use the graph of $ f'(x) $ shown and the fact that $ f(2) = 14 $ to find the value of $ f(12) $.**

## Graph Explanation

The graph presented is of the derivative $ f'(x) $ with the following characteristics:

- The horizontal axis (x-axis) is labeled from $-5$ to $12$.
- The vertical axis (f'(x) axis) is labeled from $-2$ to $8$.

### Graph Features:

1. **From $ x = -5 $ to $ x = 1 $:**
- The graph is a line decreasing from the top left to bottom right, starting at $(-5, 0)$ and ending at approximately $(1, -2)$.

2. **From $ x = 1 $ to $ x = 8 $:**
- The graph forms a semicircle, starting from $(1, -2)$, peaking at $(5, 3)$, and descending back to $(8, 0)$.

3. **From $ x = 8 $ to $ x = 12 $:**
- The graph is a line increasing sharply from $ (8, 0) $ to $ (12, 8) $.

## Multiple Choice Options

a) $ \frac{9}{2} \pi + 23 $

b) $ \frac{9}{2} \pi + 14 $

c) $ \frac{9}{2} \pi + 28 $

d) $ \frac{9}{2} \pi + 10 $

e) $ \frac{9}{2} \pi + 30 $

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 8

Step 9

Answer:

Trending now

This is a popular solution!

Step by step

Solved in 10 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Application of Differentiation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: y(x) = -0.002x2+0.7x+7 where y = vertical position of football relative to the ground (ft) x = horizontal position of football relative to launch position (ft) How high above the ground is the football as it leaves the quarterback’s hand?
Based on the following function: f (x) = -(r+ 2)² - 4 (a) What is the vertex as an ordered pair? (b) What is the y-intercept as an ordered pair?
Needed to confirm if I did this equation correctly
Find the y-intercept for the graph of the quadratic function
4) The cost of making x items is C(x)=15+2x. The cost p per item and the number made x are related by the equation p+x=25. Profit is then represented by px-C(x) [revenue minus cost]. a) Find profit as a function of x b) Find x that makes profit as large as possible c) Find p that makes profit maximum.
You manufacture ceramic lawn ornaments. After several months, your accountment tells you that your profit. P(n), can be modeled by the function P(n)= -0.002n^2 + 5.2n - 1208 where n is the number of ornaments sold each month a) How many ornaments must you make and sell in order to break even? b) How many ornaments must you make and sell in order to maximize profit? c) What is the maximum profit? d) How many ornaments must you make and sell in order to earn a profit of $1657?
The digital music industry has been growing steadily since the 2000s. The function h represents the percentage of music sales that are digital as a function of the number of years since 2002, t. 15.8182+49.91t h(t) = 17.0418+0.52t a) Determine (and state) the Vertical Intercept. Be sure to express as a point and round values to 2 decimal places. b) Explain the Vertical Intercept's meaning in the problem context. c) Determine (and state) the Horizontal Asymptote. Be sure to express your answer as a line and round values to 2 decimal places.
The total fresh vegetables consumed per person per year can be modeled by V(t) = 0.2(t- 2)² + 64.8 where V(t) is the total fresh vegetables consumed per person in pounds per year t years since 2013. Find when the minimum intake of fresh vegetables per person occurred? {final answer will be just number only}
if point (20,10) is on the graph of y=f(x). How would you Find the corresponding point on the graph of y=-2f(2(x+1))+6?
From the graph of f (x), state the reason why f (x) is discontinuous at x = 4 , x = 0 , x = 2 and x = -3.