Question

given that (view first image) and c = 3, find f ' (c) by forming the difference quotient (second image)

and taking the limit as h→0.

Answer 1

diff quotient

Answer 2

\[\lim_{h\rightarrow0}\frac{-4(c+h)-6(c+h)^2-(-4c-6c^2)}{h}=\]\[\lim_{h\rightarrow0}\frac{-4c-4h-6c^2-12ch-6h^2+4c+6c^2}{h}=\]\[\lim_{h\rightarrow0}\frac{-4h-12ch-6h^2}{h}=-4-12c=f'(c)\]\[f'(3)=-4-12\cdot3=-40\]