Question

suppose,
f(x+h)-f(x)/h = -2h(x+4)^2-h^2/h(x+h+4)^2(x+4)^2

Find the slope of the tangent line at x=3

Answer 1

\[\frac{ f(x+h)-f(x) }{ h } = \frac{ -2h(x+4)^2-h^2 }{ h(x+h+4)^2(x+4)^2 }\]

Answer 2

is this suppose to be a limit?
h->0

Answer 3

It's finding the slope of a tangent line at x=3.

Answer 4

yes i know
the first part is normally written

\[\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}\]

which is why im wondering whether or not you're missing the limit

Answer 5

they do not include the on the question, i know what you mean though

Answer 6

in that case, just divide out the h

substitute x=3 and leave all the remaining h's
and if you can simplify, then do so

Answer 7

\[-\frac{ 2x+h+8 }{ (x+4)^2(x+h+4)^2 }\] is what i get when i simplify

Answer 8

you're solving for the slope at x=3
so substitute 3 for x

Answer 9

\[\frac{ 14h }{ (49)(49h) }\]this is what i get when i plug in 3 for x

Answer 10

you made an error in calculations when doing the denominator

(x+h+4)^2
(3+h+4)^2
(7+h)^2
49+14h+h^2

adding is not the same as multiplication