   Chapter 9, Problem 61RE Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

In Problems 61 and 62, (a) find all x-values where the slope of the tangent equals zero, (b) find points (x, y) where the slope of the tangent equals zero, and (c) use a graphing utility to graph the function and label the points found in part (b). f ( x ) = x 3 − 3 x 2 + 1

(a)

To determine

To calculate: The values of x where the slope of the tangent equals zero for the function f(x)=x33x2+1.

Explanation

Given Information:

The provided function is f(x)=x33x2+1.

Formula used:

Power of x rule for function f(x)=xn is f(x)=nxn1, where n is a real number.

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x).

Constant function rule for a constant c is such that, if f(x)=c then f(x)=0.

The slope of line tangent to a curve y=f(x) at point (x1,y1) is,

m=dydx

If the product ab=0 then either a=0 or b=0.

Calculation:

Consider the function, f(x)=x33x2+1

Differentiate with respect to x

(b)

To determine

To calculate: The points (x,y) where the slope of the tangent equals zero for the function f(x)=x33x2+1.

(c)

To determine

To graph: The function f(x)=x33x2+1 with the help of a graphing utility.

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