Question

given the function:
f(x)=-2x^2-3x+6 Find: [f(x+h) -f(x)]/h, h>0

Answer 1

\[f'(x)=lim_{h\to0}\frac{f(x+h)-f(x)}{h}\]\[f'(x)=lim_{h\to0}\frac{-2*(x+h)^2-3*(x+h)+6-(-2x^2-3x+6)}{h}\]\[f'(x)=lim_{h\to0}\frac{-2*(x^2+2xh+h^2)-3x+3h+6+2x^2+3x-6}{h}\]\[f'(x)=lim_{h\to0}\frac{-2x^2-4xh-2h^2-3x+3h+6+2x^2+3x-6}{h}\]\[f'(x)=lim_{h\to0}\frac{-4xh-2h^2+3h}{h}\]\[f'(x)=lim_{h\to0}\frac{h(-4x-2h+3)}{h}\]\[f'(x)=lim_{h\to0}-4x-2h+3\]\[f'(x)=-4x+3\]

Answer 2

wait what

Answer 3

so f'(x)=-4x+3 would be the ending result?

Answer 4

Yes.

Answer 5

I think i've done enough math for today, im not even going to ask how you did it. thanks for helping

Answer 6

Are you learning about limits?!

Answer 7

And derivatives?!