Explanation It is given that the function is f ( x ) = − 5 sin 3 x . The derivative of the function is obtained as follows. d f d x = d d x ( − 5 sin 3 x ) = − 5 cos 3 x d d x ( 3 x ) = − 5 cos 3 x ( 3 ) = − 15 cos 3 x Thus, the derivative is − 15 cos 3 x . Obtain the critical numbers by setting f ′ ( c ) = 0 . − 15 cos 3 x = 0 cos 3 c = 0 cos 3 c = cos ( n π 2 ) , n = ± 1 , ± 3 , ± 5 , ... 3 c = n π 2 , n = ± 1 , ± 3 , ± 5 , ... That is, c = n π 6 , n = ± 1 , ± 3 , ... . However, the function is defined at c = ± π 6 , ± π 2 , ± 5 π 6 , ...

11th Edition

ISBN: 2818440028601

Author: Lial

Publisher: XX SUPPLY

See similar textbooks

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Videos

Question

Chapter 13, Problem 62RE

To determine

The locations and values of all relative extrema.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13, Problem 61RE

Chapter 13, Problem 63RE

Students have asked these similar questions

Q1: A slider in a machine moves along a fixed straight rod. Its distance x cm along the rod is given below for various values of the time. Find the velocity and acceleration of the slider when t = 0.3 seconds. t(seconds) x(cm) 0 0.1 0.2 0.3 0.4 0.5 0.6 30.13 31.62 32.87 33.64 33.95 33.81 33.24 Q2: Using the Runge-Kutta method of fourth order, solve for y atr = 1.2, From dy_2xy +et = dx x²+xc* Take h=0.2. given x = 1, y = 0 Q3:Approximate the solution of the following equation using finite difference method. ly -(1-y= y = x), y(1) = 2 and y(3) = −1 On the interval (1≤x≤3).(taking h=0.5).

Consider the function f(x) = x²-1. (a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative. Show all your steps clearly. (b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the graph where x 1 and x-> 1+h (for a small positive value of h, illustrate conceptually). Then, draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the value you found in part (a). (c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in the context of the graph of f(x). How does the rate of change of this function vary at different points?

1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist, state that fact. и (a) f'(-5) (b) f'(-3) (c) f'(0) (d) f'(5) 2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5) = 4. - 3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2) and f'(2).

Chapter 13 Solutions

CALCULUS WITH APPLICATIONS

Ch. 13.1 - (a) Convert 210° to radians. (b) Convert 3π/4...Ch. 13.1 - Find the values of the six trigonometric functions...Ch. 13.1 - Prob. 3YT Ch. 13.1 - Prob. 4YT Ch. 13.1 - Find all values of θ between 0 and 2π that satisfy...Ch. 13.1 - Convert the following degree measures to radians....Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Convert the following degree measures to radians....Ch. 13.1 - Prob. 5E

Knowledge Booster

$Calculus$

Learn more about

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