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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

If g(x) = xf(x), where f(3) = 4 and f'(3) = –2, find an equation of the tangent line to the graph of g at the point where x = 3.

To determine

To find: The equation of the tangent line to the graph at the point.

Explanation

Given:

The function g(x)=xf(x).

The point is x=3.

Derivative rule:

Product Rule: ddx[f1(x)f2(x)]=f1(x)ddx[f2(x)]+f2(x)ddx[f1(x)]

Formula used:

The equation of the tangent line at (x1,y1) is, yy1=m(xx1) (1)

Here, m is the slope of the tangent line at (x1,y1) and m=dydx|x=x1.

Calculation:

Obtain the slope of tangent to the function g(x) at x=3.

The derivative of g(x) at x=3 is computed as follow,

g(x)=ddx(xf(x))

Apply the product rule (1) and simplify the terms,

g(x)=xddx(f(x))+f(x)dd

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