   Chapter 9.4, Problem 17E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 15-18, at the indicated points, find(a) the slope of the tangent to the curve.(b) the instantaneous rate of change of the function. P ( x ) = x 3 − 6 x ,  (2,-4)

(a)

To determine

To calculate: The slope of the tangent to curve P(x)=x36x at (2,4).

Explanation

Given Information:

The provided curve is represented by function P(x)=x36x and the point is (2,4).

Formula Used:

The slope of line tangent to the curve y=f(x) at any point x is f(x).

Difference rule for function f(x)=u(x)v(x), where u and v are differentiable functions of x, then f(x)=u(x)v(x).

Power of x rule for a real number n is such that, if f(x)=xn then f(x)=nxn1.

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.

Calculation:

Consider the function, P(x)=x36x

Differentiate with respect to x

(b)

To determine

To calculate: The instantaneous rate of change of the function P(x)=x36x at (2,4).

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