Explanation Given: The given function is f ( x ) = 3 x 5 / 3 − 15 x 2 / 3 . Approach: The first derivative test: The f ( c ) is a relative maximum of function f if the derivative f ′ ( x ) is positive in the interval ( a , c ) and negative in the interval ( c , b ) . The f ( c ) is a relative minimum of function f if the derivative f ′ ( x ) is negative in the interval ( a , c ) and positive in the interval ( c , b ) . Calculation: Consider the given function: f ( x ) = 3 x 5 / 3 − 15 x 2 / 3 Differentiate the above function with respect to x : f ′ ( x ) = d d x ( 3 x 5 / 3 − 15 x 2 / 3 ) = d d x ( 3 x 5 / 3 ) − d d x ( 15 x 2 / 3 ) = 5 x 2 / 3 − 10 x 1 / 3 There are exist points x = 0 where f ′ ( x ) fail to exist, so the only critical numbers will found where derivative equal to zero. 5 x 2 / 3 − 10 x 1 / 3 = 0 ( 5 x − 10 ) = 0 The critical number x = 0 and x = 2 are used to determine three interval ( − ∞ , 0 ) , ( 0 , 2 ) and ( 2 , ∞ )

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

2nd Edition

ISBN: 9780137553457

Author: Raymond Greenwell, Nathan Ritchey

Publisher: PEARSON+

See similar textbooks

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 ter…

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 …

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 …

Videos

Question

Chapter 5.2, Problem 24E

To determine

To find:

The all relative extrema of the function f(x)=3x5/3−15x2/3.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5.2, Problem 23E

Chapter 5.2, Problem 25E

Students have asked these similar questions

i need help please

slove the initial-value problem. y'' + 7y' + 12y = 0, y(0) = 2, y'(0) = 8

Chapter 5 Solutions

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

Ch. 5.1 - YOUR TURN Find where the function is increasing...Ch. 5.1 - YOUR TURN 2 Find the intervals in which...Ch. 5.1 - Prob. 3YT Ch. 5.1 - YOUR TURN Find where f is increasing and...Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Find the open intervals where the functions...Ch. 5.1 - Prob. 6E

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.