Question

If h(2) = 3 and h'(2) = −6, find

Answer 1

tangent line at x=2?

Answer 2

\[\frac{ d }{ dx }\(\frac{ h(x) }{ x }) x=2\]

Answer 3

yes

Answer 4

are you sure?
what is that you are writing?

Answer 5

Did you mean to write h(x) / x ?

Looks like too many x's 0_o

Answer 6

\[\frac{d}{dx} (\frac{h(x)}{x})=2\]?

Answer 7

ill take a screen shot

Answer 8

do you know how to use the quotient rule or even the product rule will work (if we rewrite it as a product)

Answer 9

i have it in my notes but i don't feel confident enough to do it on my own

Answer 10

\[\frac{d}{dx}(h(x)x^{-1})=(h(x))'(x^{-1})+(h(x)) (x^{-1})' \text{ by product rule } \]

Answer 11

find the derivative of x^(-1)
derivative of h is easy it is h'

Answer 12

what would our first step be then for solving the problem

Answer 13

finding the derivative of x^(-1)

Answer 14

okay how do we do that then.. lol

Answer 15

power rule

Answer 16

so then move the number over pass the x and then subtract exponents by 1

Answer 17

yes and that gives you?

Answer 18

\[\frac{d}{dx}(h(x)x^{-1})=(h(x))'(x^{-1})+(h(x)) (x^{-1})' \text{ by product rule } \]
when you are done you can replace the (x^(-1))' with what you fund for it

Answer 19

found*

Answer 20

once you found the derivative
your next is to replace the x's with 2's
and to recall what h(2) and h'(2) was

Answer 21

and then order of operations