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Chapter 2: Q. 15 (page 124)

Find the different quotients off(x)=-2x2+x+1;that is,find f(x+h)-f(h)h,h鈮�0

Short Answer

Expert verified

The difference quotient is-4x+1-2h

Step by step solution

01

Step 1.Given information

The given Function f(x)=-2x2+x+1

we have to find f(x+h)-f(x)h

02

Step 2.Compute the given function 

Substitute (x+h)for x in the equation,f(x)=-2x2+x+1to obtain f(x+h)

f(x+h)=-2(x+h)2+(x+h)+1

Now compute the function f(x-h)-f(x)h

f(x+h)-f(x)h=(-2(x+h)2+(x+h)+1)-(-2x2+x+1)h=(-2(x2+2xh+h2)+x+h+1)-(-2x2+x+1)h=(-2x2-4xh-2h2+x+h+1+2x2-x-1)h

03

Step 3.Combine the like terms and simplify

-2x2-4xh-2h2+x+h+1+2x2-x-1h=(2-2)x2(1-1)x+(1-1)-4xh-2h2+hh=-4xh+h+-2h2h=-4xh+1-2h

Therefore,the difference quotient is-4x+1-2h

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