For the function f ( x ) = 3x^2 − 2x − 7

Question

For the function f(x)= 3x^2 −2x −7, evaluate and fully simplify each of the following.

f (x+h) =

f(x+h)-f(x)/h =

Answer 1

f(x) = 3x²-2x-7

f(x+h) = 3(x+h)² - 2(x+h) -7

= 3( x² + 2xh + h² ) - 2x - 2h -7

= 3x² + 6xh + 3h² -2x -2h -7

f(x + h ) - f (x) / h = 3x² + 6xh + 3h²-2x -2h -7 - 3x² + 2x +7 /h

= 3x² - 3x² - 2x + 2x -7 +7 +6xh -2h +3h²/h

= h ( x - 2 + 3h ) / h

= x - 2 + 3h