   Chapter 10.6, Problem 39E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises39-44, find the equation of the tangent to the graph at the indicated point. [HINT: Compute the derivative algebraically; then see Example 2(b) of Section 10.5.] f ( x ) = x 2 − 3 ; a = 2

To determine

To calculate: The tangent line equation for the function f(x)=x23 at the indicated point a=2.

Explanation

Given information:

The function is f(x)=x23 and the indicated point on which slope has to be determined is a=2.

Formula used:

The slope of the tangent line passing through the point x=a on the function f(x) is equal to the derivative f(a), that is mtan=f(a)=limh0f(a+h)f(a)h.

The equation of tangent line passing through a point and having slope is y=mx+b.

Calculation:

Consider the function f(x)=x23

The slope of the tangent line passing through the point x=a on the function f(x) is,

m=f(a)=limh0f(a+h)f(a)h

Substitute a=2 in the above formula,

m=f(2)=limh0f(2+h)f(2)h

Here f(2)=(2)23 then,

f(2+h)=(2+h)23

Substitute the values of f(2) and f(2+h) in the function limh0f(2+h)f(2)h as,

m=limh0[(2+h)23

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