   Chapter 11.3, Problem 74E ### 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 Exercises 71-76, find the equation of the line tangent to the graph of the given function at the point with the indicated x-coordinate. f ( x ) = x + 1 x + 2 ; x = 4

To determine

To calculate: The equation of the tangent to the graph of the function f(x)=x+1x+2 at x=4.

Explanation

Given Information:

The function is f(x)=x+1x+2 and x=4.

Formula used:

Quotient rule:

If f(x) and g(x) are differentiable functions, then

ddx[f(x)g(x)]=f'(x)g(x)f(x)g'(x)[g(x)]2, where g(x)0.

Power rule:

For a function f(x)=xn,

f'(x)=nxn1, where n is some constant.

Sum rule of derivative:

ddx[f(x)+g(x)]=ddx[f(x)]+ddx[g(x)]

Where, f(x) and g(x) are any two differentiable functions.

Slope of tangent of graph f(x) at point (a,b) is given by:

f'(a)

Equation of line is y=mx+b where m is the slope and b=y1mx1 when line passes through (x1,y1).

Calculation:

Consider the function, f(x)=x+1x+2.

Find slope of tangent of graph f(x)=x+1x+2 by determining derivative of the function f(x).

Rewrite the function,

f(x)=x12+1x12+2

Apply quotient rule to the function,

f'(x)=[ddx(x12+1)](x12+2)(x12+1)[ddx(x12+2)](x12+2)2

Apply sum rule of derivative,

f'(x)=[ddx(x12)+ddx(1)](x12+2)(x12+1)[ddx(x12+2)](x12+2)2

Apply power rule,

f'(x)=(12x121+0)(x12+2)(x12+1)(12x121+0)(x12+2)

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