Question

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Answer 1

Find the derivative of f(x) = 8x^2 + 11x at x = 7.

Answer 2

for starters, so do you know how you can get the derivative of just x^2 ?

Answer 3

I know it is the formula \(\dfrac{f(x) - f(x+h)}h\), but I'm not sure how to use that...

Answer 4

Its
\(f'(x) = \lim \limits_{h \to 0}\dfrac{f(x+h) - f(x)}h\)

Answer 5

\(\dfrac{x^2 - (x^2+h)}h\)?

Answer 6

if you're using that, lets take
8x^2 + 11x only

so f(x) = 8x^2 + 11x
how about f(x+h) = ... ?

just replace all x's with x+h

Answer 7

Okay....
\(\dfrac{(8(x+h)^2 + 11(x+h))-8x^2+11x}h\)

Answer 8

correct! go on, and simplify the numerator ..

Answer 9

\(\dfrac{8x^2+8h^2+16xh + 11x+11h-8x^2-11x}h\)?
\(\dfrac{8h^2+16xh +11h}h\)?

Answer 10

wow you're good at this! :)

Answer 11

really? O.o

Answer 12

yeah, because thats correct

now just simplify each term,

8h^2/h = .. ?
16xh/h = .. ?
11h/h = ... ?

Answer 13

8h+16x+11

Answer 14

correct, and since h->0
you just plug in h = 0 in that

Answer 15

what about x though?

Answer 16

would I plug in 7 for x?

Answer 17

yes,
but lets first state that

f'(x) = 16x+11

and you need it at x=7, so then plug x=7 in it :)

Answer 18

you iz so good at math <3

Answer 19

you'll become so good too :)

Answer 20

maybe in your dreams :P

Answer 21

so won't you wanna make my dreams come true? ;)

Answer 22

I ain't that smart :P