Question

Help! Suppose that (f(x+h)-f(x))/h = (-2h(x+4)-h^2)/h(x+h+4)^2(x+4)^2

Find the slope m of the tangent line at x+1.
m=?

Answer 1

at \(x=1\) ?

Answer 2

Yes sorry I typed it wrong

Answer 3

replace \(x\) by \(1\) and compute the limit

Answer 4

is it \[\frac{-2h(x+4)-h^2}{h(x+h+4)^2(x+4)^2} \]??

Answer 5

Yes

Answer 6

then start with
\[\frac{-2h(1+4)-h^2}{h(1+h+4)^2(1+4)^2}\]

Answer 7

\[\frac{-10h-h^2}{h(h+5)^2\times 25}\]

Answer 8

I got that. Then I simplified the bottom.

Answer 9

\[\frac{h(-10-h)}{25h(h+5)^2}=\frac{-10-h}{25(h+5)^2}\] now replace \(h\) by zero to get your answer

Answer 10

don't multiply out, that is a bad idea
factor and cancel the \(h\) so you can replace \(h\) by \(0\) without getting a zero in the denominator

Answer 11

O ok.

Answer 12

I got
m= -10/625