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Forf(x)=-3x2+5x-2,findf(x+h)-f(x)h,h≠0

Short Answer

Expert verified

The required answer is-6x-3h+5

Step by step solution

01

Step 1. Given Information

The given function isf(x)=-3x2+5x-2

02

Step 2. Calculation

Substitute x+hforxin the given function and expand the expression.

f(x+h)=-3(x+h)2+5(x+h)+2=-3(x2+2xh+h2)+5x+5h+2=-3x2-6xh-3h2+5x+5h+2

Substitute the values in the expression f(x+h)-f(x)hand simplify.

f(x+h)-f(x)h=(-3x2-6xh-3h2+5x+5h+2)-(-3x2+5x+2)h=-6xh-3h2+5hh=-6x-3h+5

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