Evaluating a Difference Quotient In Exercises 8386 find the

Evaluating a Difference Quotient In Exercises 83-86, find the difference quotient and simplify your answer. g(x) = 3x -1, g(x + h) - g (x)/h h = 0 f(x) = x^2 - x + 1, f(2 + h) - f(2)/h, h = 0

Solution

for
(84) g(x) = 3x-1 , {g(x+h)-g(x)}/h
I need to plug the expression \"x + h\" in for every \"x\"
so g(x+h) = 3(x+h)-1 , g(x) is mention clearly (3x-1).
Putting all the values we got
{g(x+h)-g(x)}/h = {3(x+h)-1 -(3x-1)}/h
= (3x + 3h -1 -3x + 1)/h
= 3

for
(85) f(x) = x^2-x+1 , [f(2+h)-f(2)]/2
I need to plug the expression \"2 + h\" in for every \"x\"
than \"2\" for every x
f(x) = x^2-x+1
f(2+h) = 4+h^2+4h-(2+h)+1
= 3+h^2+3h
similiarly f(2)
f(x) = x^2-x+1
f(2) = 2^2-2+1 = 3
Putting all the values we get
[f(2+h)-f(2)]/2 = [3+h^2+3h-3]/h
= h+3
Answer