Question

find the difference quotient f(x+h)-f(x)/h for the function f (x)=-3x^2+7x-2.
a) -6x-6h+7
b) -6x-3h+7
c) -6x-3h+7-6x^2+14x-4/hx
d) -6x-6h+5
e) none of the above

Answer 1

b

Answer 2

explain please?

Answer 3

\[\frac{f(x+h)-f(x)}{h}=\frac{-3(x+h)^2+7(x+h)-2-(-3x^2+7x-2)}{h}\]

\[=\frac{-3(x+h)^2+7(x+h)-2+3x^2-7x+2}{h}\]
\[=\frac{-3x^2-6xh-3h^2+7x+7h-2+3x^2-7x+2}{h}\]
\[=\frac{-6xh-3h^2+7h}{h}=-6x-3h+7\]