   Chapter 9.3, Problem 28E ### 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 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 ) . ( − 1 , 6 ) ; x + 10 y = 59

To determine

To calculate: The value of f'(a) and f(a) if (a,b)=(1,6) is a point on y=f(x) which lies on the tangent line x+10y=59.

Explanation

Given Information:

It is provided that (a,b)=(1,6) is a point on y=f(x) which lies on the tangent line x+10y=59.

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=f(a)

Calculation:

Consider the provided statement,

The (a,b)=(1,6) is a point on y=f(x) which lies on the tangent line x+10y=59.

The value of b=6 at a=1

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