Explanation Given: Function f ( x ) = 3 x 5 − 5 x 3 Formula Used: Critical points of the function are the points where the function is defined and its derivative is undefined or zero. Let us assume that p is the critical point of a continuous function f . Moving from left to right If p′ changes from negative to positive at p , then f has local minimum at p If p′ changes from positive to negative at p , then f has local maximum at p Calculation: Function is given as f ( x ) = 3 x 5 − 5 x 3 The graph of the above function is as follows: From the graph, we see that There are threecritical point Also, function is an increasing, when x < − 1 and x > 1 The function is decreasing when − 1 < x < 1 Derivative of above function is calculated as follows: f ′ ( x ) = d d x ( 3 x 5 − 5 x 3 ) f ′ ( x ) = 3 (

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Chapter 4.1, Problem 16P

To determine

To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative

f(x)=3x5−5x3

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Chapter 4.1, Problem 15P

Chapter 4.1, Problem 17P

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3. Differentiate the following functions. Show your work where applicable. a) y = e³x b) f(x)=2 cos(5x) c) y = 1 - 2 d) y = In|secx| e) f(t) = t² e√t f) f(x) = 1+x x sin x 3

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Please help on both Part b) and c) below Thanks

Chapter 4 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative f ( x ) = 3 x 5 − 5 x 3

Solution Summary: The author explains the function's critical points and its derivative, which is undefined or zero.

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To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative

f(x)=3x5−5x3

Want to see the full answer?

Chapter 4 Solutions

To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative f ( x ) = 3 x 5 − 5 x 3

Solution Summary: The author explains the function's critical points and its derivative, which is undefined or zero.

Concept explainers

Videos

To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative f(x)=3x5−5x3

Want to see the full answer?

Chapter 4 Solutions

To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative

f(x)=3x5−5x3