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Chapter 14: Q. 19 (page 897)

In Problems 9鈥�20, find the slope of the tangent line to the graph of f at the given point. Graphf and the tangent line.

f(x)=x3+xat2,10

Short Answer

Expert verified

The slope of tangent is 13.

The graph is as follows,

Step by step solution

01

Step 1. Given Information 

We are given a function,

f(x)=x3+x

We have to find the slope of the tangent line and graph the function and tangent line.

02

Step 2. Finding the slope 

The slope is given by,

mtan=limx鈫�ef(x)-f(c)x-c

Putting the values, we get

m=limx鈫�2f(x)-f(2)x-(2)=limx鈫�2x3+x-10x-2=limx鈫�2x2+2x+2(x-2)x-2=limx鈫�2x2+2x+5=22+2(2)+5=4+4+5=13

Hence the slope of tangent is 13.

03

Step 3. Graphing the function 

The equation of tangent is given by,

y-y1=mx-x1y-10=13(x-2)y=13x-26+10y=13x-16

The graph is as follows,

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