(a) Using a graphing utility, graph f1x2 = x3 - 4x for- 3 ... x ... 3.(b) Find the x-intercepts of the graph of f.(c) Approximate any local maxima and local minima.(d) Determine where f is increasing and where it is decreasing.(e) Without using a graphing utility, repeat parts (b)–(d) fory = f1x - 42.(f) Without using a graphing utility, repeat parts (b)–(d) fory = f12x2.(g) Without using a graphing utility, repeat parts (b)–(d) fory = - f1x2.

Q: Which of the following is a point on the graph of the function 5 - 3x f(x) = 4. (-5, 5) (2,-1) (1.4)…

A:

Q: Graph f(x) = 2|x + 1| + 4|x 5-20 with a graphing calculator in the window [-10, 10] by [-15, 30].…

A: Given that, fx=2x+1+4x-5-20      ...(1)

Q: Sketch the graph of f ( x ) = 2x³ - 3x² + 3 , indicating the points of inflection and the intervals…

A:

Q: What function equation is represented by the graph? o f(x) = -žx+ o f(x) = -x+4 of (x) = -4x + of…

A: Two points that are on the graph are (0,4),(2.-1)

Q: Based on the graph what is the value of f (4)

A: Solution: The objective is to find the value of f(4) from the given graph

Q: Move the sliderk so that the graph of y = 2" gets shifted up 3 units. Then type the new function,…

A: We have to slide the k such that graph shifted 3 unit up.

Q: Stefan saud that the y-intercept for the graph of the function f(X)=3log(x-7)+1 is 1. He also said…

A: Stefan said: 1. the y-intercept for the graph of the function fx=3logx-7+1 is 1. 2. the x approaches…

Q: The integral of 2 raised to 4x dx with limits of 1 to 2 is equal to 85.6521 86.5617 86.1657 85.5621…

A:

Q: For the function whose graph is shown below, at which value of x is the graph continuous and…

A: Sol

Q: Graph of the function f(x) = x+a/ x^2 + bx +4 is shown below. What are a and b?

A: Answer

Q: ƒ (x) = − ½-|x| − 14x^8 +7   is this a function if so how and why

A:

Q: a) ƒ' (x) = = 1 for all 0 ≤ x ≤ 4. b) f'(x) > 0 for all 0 ≤ x ≤ 4. c) f' (3) = 0 d) f' (3) = 1 > > >

A:

Q: 4) Suppose that x thousand units of a product will be sold when the price is p(x) = -2x + 31 dollars…

A: Please see the explanation below

Q: How to graph f(x)=|x+1|

A: To draw the graph of the following function.

Q: Sketch the graph of:

A:

Q: 38. A rectangle is inscribed in a semicircle with diameter 10 centimeters as shown. Express the area…

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Q: Use the following graph of f(x) to sketch the graph of f(x-2)-3.

A: The graph of f(x) is given.

Q: -100t i= 2 -20 [-2 +2e" - 200te-100t -100(t-1) + 200 (t-1) e

A: First draw the graph of 2-2e-100t-200te-100t for 0≤t≤1.

Q: Determine where the graph of f(x) = |x - 3| is increasing and where it is decreasing.

A: To determine: The intervals where the function f(x)=x-3is increasing and decreasing. Given…

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.