Given f(x)=x^2 -3x +4

Question

Find

f(2+h)

Find

f(2+h)-f(2)/h

Answer 1

To find f(2 +h), substitute (2 + h) for every x

f(2+h) = (2 + h)² - 3( 2 + h) + 4 simplify

f(2 + h) = 4 + 4h + h² + 4

f(2 +h) = h² +4h + 8

f(2) = 2² - 3(2) + 4 = 4 - 6 + 4 = 2

f(2 +h) - f(h) / h =( h² + 4h +8 - 2 )/h then simplify

Answer 2

f(x) = x^2 -3x +4

f(2) = 4-6+4 = 2

f(2+h) = h^2 + 2h + 4 - 3h - 6 + 4 = h^2 -h +2

h(2+h)-h(2) = h^2 -h

(h(2+h) -h(2))/h = h-1

sort of a check on the answer

compare the 1st derivative

f'(x) = 2x -3

f'(2) = 2(2)-3 = -1 when h goes to zero