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Chapter 14: Q. 18 (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)=-2x2+x-3at(1,-4)

Short Answer

Expert verified

The slope of tangent is -3.

The graph is as follows,

Step by step solution

01

Step 1. Given Information

We are given a function,

f(x)=-2x2+x-3

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�cf(x)-f(c)x-c

Putting the values, we get

role="math" localid="1647076630300" m=limx鈫�1f(x)-f(1)x-(1)=limx鈫�1-2x2+x-3-(-4)x-1=limx鈫�1-2x2+x-3+4x-1=limx鈫�1-2x2+x+1x-1=limx鈫�1(-2x-1)(x-1)x-1

03

Step 3. Finding the limit

Finding the limit,

m=limx鈫�1(-2x-1)m=-2(1)-1m=-2-1m=-3

Hence the slope of tangent is -3.

04

Step 4. Graphing the function

The equation of tangent is given by,

y-y1=mx-x1y-(-4)=-3(x-1)y+4=-3x+3y=3x-1

The graph is as follows,

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