Chapter 9.3, Problem 27E

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# In Problems 27 and 28, a point ( a , b ) on the graph of y =   f ( x ) is given, as is the equation of the line tangent to the graph of f ( x ) at ( a ,   b ) . In each case, find f ' ( a ) and f ( a ) . ( 4 , − 11 ) ; 7 x − 3 y = 61

To determine

To calculate: The value of f'(a) and f(a) if (a,b)=(4,11) is a point on y=f(x) which lies on the tangent line 7x3y=61.

Explanation

Given Information:

It is provided that (a,b)=(4,âˆ’11) is a point on y=f(x) which lies on the tangent line 7xâˆ’3y=61.

Formula used:

If straight line is defined as y=mx+c, then m is the slope of the tangent and c is the intercept.

The function y=f(x) has tangent line y=mx+c at point (a,b) then;

m=fâ€²(a)

Calculation:

Consider the provided statement,

The (a,b)=(4,âˆ’11) is a point on y=f(x) which lies on the tangent line 7xâˆ’3y=61

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