Question

HELPPPP!!!
find the difference quotient and simplify

Answer 1

can you show me how to work this out

Answer 2

@satellite73

Answer 3

\[f(x)=5x-x^2\]
\[f(5)=5\times 5-5^2=25-25=0\]
\[f(5+h)=5(5+h)-(5+h)^2=25+5h-(25+10h+h^2)\]
\[=25+5h-25-10h-h^2=-5h+h^2\]

Answer 4

and so
\[f(5+h)-f(5)=-5h+h^2-0=-5h+h^2\] therefore
\[\frac{f(5+h)-f(5)}{h}=\frac{-5h+h^2}{h}=\frac{h(-5+h)}{h}=-5+h\]

Answer 5

thank you, so the final answer is -5+h not -5+h^2?

Answer 6

@satellite73, shouldn't \[f(5+h) =-5h-h^2\]