   Chapter 9.5, Problem 9E ### 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 9 and 10, at each indicated point, find(a) the slope of the tangent line.(b) the instantaneous rate of change of the function. y =( x 2 + 1 )( x 3 − 4 x )  at ( − 2,0)

(a)

To determine

To calculate: The slope of the tangent line whose function is y=(x2+1)(x34x) at point (2,0).

Explanation

Given Information:

The function is y=(x2+1)(x34x)

Formula Used:

The product rule for the derivative of the two function f(x) and g(x) is, ddx(fg)=fdgdx+gdfdx.

The sum and difference rule of derivate of functions, ddx[u(x)±v(x)]=ddxu(x)±ddxv(x).

The simple power rule of derivative ddx(xn)=nxn1.

Calculation:

Consider the provided function is y=(x2+1)(x34x).

Differentiate the provided function with respect to x.

dydx=ddx[(x2+1)(x34x)]

Use the product rule for the derivative of the two function f(x) and g(x) is, ddx(fg)=fdgdx+gdfdx.

dydx=(x2+1)ddx(x34x)+(x34x)ddx(x2+1)

Use the sum and difference rule of derivate of functions, ddx[u(x)±v(x)]=ddxu(x)±ddxv(x)

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