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Chapter 14: Q. 20 (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-x2at1,0

Short Answer

Expert verified

The slope of tangent is 1.

The graph is as follows,

Step by step solution

01

Step 1. Given Information 

We are given a function,

f(x)=x3-x2

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�1f(x)-f(1)x-(1)=limx鈫�1x3-x2-0x-1=limx鈫�1x2(x-1)x-1=limx鈫�1x2=12=1

Hence the slope of tangent is 1.

03

Step 3. Graphing the function 

The equation of tangent is given by,

y-y1=mx-x1y-0=1(x-1)y=x-1

The graph is as follows,

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