   Chapter 2.7, Problem 22E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# If the tangent line to y= f(x) at (4, 3) passes through the point (0, 2), find f(4) and .f'(4).

To determine

To find: The value of the functions f(x) and f(x) at x=4.

Explanation

Given:

The equation of the curve is y=f(x).

The tangent line to y=f(x) at (4, 3) passes through the point (0, 2).

Formula used:

The slope of the tangent line between two points (x1,y1) and (x2,y2) is,

m=y2y1x2x1 (1)

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.”

Calculation:

Obtain the function f(x) at 4.

Given that the tangent line to y=f(x) at (4, 3) passes through the point (0, 2).

Clearly the point (4, 3) lies on the curve y=f(x)

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