Chapter 4.3, Problem 69E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Finding and Analyzing Derivatives Using Technology In Exercises 63-70, (a) use a computer algebra system to differentiate the function, (b) sketch the graphs of f and f' on the same set of coordinate axes over the given interval, (c) find the critical numbers of f in the open interval, and (d) find the interval(s) on which f is positive and the interval(s) on which f' is negative. Compare the behavior of f and the sign of f'. f ( x ) = 1 2 ( x 2 − ln x ) ,       [ 0 , 3 ]

(a)

To determine

To calculate: The derivative of the function f(x)=12(x2lnx).

Explanation

Calculation:

Use Maple to obtain the derivative of the function.

Maple command

(b)

To determine

To graph: The function f(x)=12(x2lnx) and its derivative in the same coordinate axes.

(c)

To determine

To calculate: The critical numbers for the function f(x)=12(x2lnx) that lie in the interval (0,3).

(d)

To determine

To calculate: The sub-intervals for which the derivative of the function f(x)=12(x2lnx) is positive or negative. Also compare the conduct of f and f’.

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