Question

Can someone help me with this function problem (see attachment)

Answer 1

Essentially you are taking the first derivative but they want you to work it out the long way

Answer 2

\[f(x+h)=-3(x+h)^2-4(x+h)-4\]\[=-3(x^2+2hx+h^2)-4x-4h-4\]\[=-3x^2-6hx-3h^2-4x-4h-4\]
\[\frac{-3x^2-6hx-3h^2-4x-4h-4-(-3x^2-4x--4)}{h}\]\[=\frac{-6hx-3h^2-4h}{h}\]\[=\frac{h(-6x-3h-4)}{h}\]\[=-6x-3h-4\]

Answer 3

\[(-3(x+h)^2 - 4(x+h)-4 - (-3x^2 - 4x - 4))/h\]
\[(-3(x^2+2xh+h^2) - 4(x+h)-4 +3x^2 + 4x + 4)/h\]
\[(-3x^2-6xh-3h^2 - 4x-4h-4 +3x^2 + 4x + 4)/h\]
\[(-6xh-3h^2 -4h)/h = -6x-3h-4\]

Answer 4

For the first derivative you will take the limit as h approaches zero which will make the equation simplify to\[ -6x-4\]