Question

Find f(x + h) when f(x) = -3x^2 - 2x + 4.

A. -3x^2 - 3h^2 - 2x - 2h + 4
B. -3x^2 - 3h^2 - 8x - 8h + 4
C. -3x^2 - 3xh - 3h^2 - 2x - 2h + 4
D. -3x^2 - 6xh - 3h^2 - 2x - 2h + 4

Answer 1

You’re learning the definition of the derivative aren’t you. Just plug in x+h and do FOIL. Then multiply each term by -3 because of -3 infront of the square.
-3(x+h)^2 - 2(x+h) +4
-3[x^2 + 2xh + h^2] - 2x - 2h + 4
-3x^2 - 6xh - 3h^2 - 2x - 2h + 4
Your answer is D