   Chapter 2.7, Problem 20E

Chapter
Section
Textbook Problem

Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = –3 and g'(5) = 4.

To determine

To find: The equation of the tangent line to the graph of y=g(x) at x=5.

Explanation

Given:

The function g(x) at x=5 is −3. That is, the point (5, −3) lies on the curve y=g(x).

The derivative of the function g(x) at x=5 is 4. That is, g(5)=4.

Formula used:

Result 1:

“The tangent line to y=f(x) at (a,f(a)) is the line through (a,f(a)) whose slope is equal to f(a), the derivative of f at a.”

The equation of the tangent line to the curve y=f(x) at the point (a,f(a)) is,

yf(a)=f(a)(xa) (1)

Calculation:

Obtain the equation of the tangent line to the graph of y=g(x) at x=5.

The function y=g(x) passes through the point (5, −3) and the derivative g(5)=4

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