Find the difference quotient of f;that is; find f(x+h)-f(x)/ h doesnt =0
f(x)=-2x+6
First, find the values of f(x+h) and f(x) so they can be substituted into the difference quotient f(x+h)-f(x)/h
f(x+h)=-2(x+h)+6
Simplify. What is the value of f(x+h)?
f(x+h)=-2x-2h+6
It is given that f(x)=-2x+6.
Substitute f(x+h)=-2x-2h+6 and f(x)=-2x+6 into the difference quotient f(x+h)-f(x)/h
f(x+h)-f(x)/h = (-2x-2h+6)-(-2x+6)/h
= -2x-2h+6+2x-6/h
Now, simplify completely. What is the result?
f(x+h)-f(x)/h = -2
Therefore, f(x+h)-f(x)/h = -2 when f(x) =-2x+6
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