Question

For the function:
F(x)= 3x^2+10x+1
compute the difference quotient : [F(x+h)-f(x)] h

H isn't equal to 0. Attempt to simplify your answer.

I got the couple before this right, but keep on getting this one wrong. Can a kind someone show me the steps please, thanks!

Answer 1

\[\frac{3(x+h)^2+10(x+h)+1-(3x^2+10x+1)}{h}\] is a start

Answer 2

then
\[\frac{3(x^2+2xh+h^2)+10x+10h+1-3x^2-10x-1}{h}\]
distribute
\[\frac{3x^2+6xh+3h^2+10x+10h+1-3x^2-10x-1}{h}\]
usual miracle everything without an "h" adds up to zero
\[\frac{6xh+3h^2+10h}{h}\]
divide each term by h
\[6x+10+3h\]

Answer 3

\[\frac{3h^2+6hx+10h}{h}=\frac{3h^{\cancel{2}}}{\cancel h}+\frac{6\cancel hx}{\cancel h}+\frac{10\cancel h}{\cancel h}= \large 3h+6x+10\]

Answer 4

thank you both so much!

Answer 5

yw