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 (

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Chapter 4.1, Problem 16P

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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

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Chapter 4.1, Problem 15P

Chapter 4.1, Problem 17P

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According to Newton's law of universal gravitation, the force F between two bodies of constant mass GmM m and M is given by the formula F = , where G is the gravitational constant and d is the d² distance between the bodies. a. Suppose that G, m, and M are constants. Find the rate of change of force F with respect to distance d. F' (d) 2GmM b. Find the rate of change of force F with gravitational constant G = 6.67 × 10-¹¹ Nm²/kg², on two bodies 5 meters apart, each with a mass of 250 kilograms. Answer in scientific notation, rounding to 2 decimal places. -6.67x10 N/m syntax incomplete.

Chapter 4 Solutions

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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

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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