Question

Find the derivative of f(x) = -2x^2 + 11x at x=9

Answer 1

can someone help me solve this while we use the formula
\[\lim_{h \rightarrow 0} \frac{ f(x+h)-f(x) }{ h } \]

Answer 2

I somehow do not know how to set it up properly

Answer 3

can you help me @Loser66

Answer 4

f(x+h)=??

Answer 5

f(x+h) = -2(x+h)^2+11x?

Answer 6

\(f(x+h)= -2(x+h)^2 +11(x+h)\)

Answer 7

why is there another (x+h)? what about the -f(x) part?

Answer 8

because f(x) = -2x^2 +11x
hence, when replace x by x +h, you MUST replace all x on the expression

Answer 9

okay, so instead of x its (x+h), but in the formula are we still going to use the other top half -f(x)?

Answer 10

would it be -2(x+h)^2+11(x+h) - (-2x^2+11x)/ h?

Answer 11

yup, open parentheses, simplify . What do you have?

Answer 12

okay let me see

Answer 13

-4hx - 2h^2 + 11h?

Answer 14

you forgot h at the denominator. That is just numerator.
From it, factor h out, cancel out with h in denominator, what do you have?

Answer 15

yeah i meant just the numerator lol

Answer 16

if i cancel the h, i would have -4x - 2h + 11

Answer 17

would i now replace h with 0?

Answer 18

Hold on, your calculation is not correct. Let check

Answer 19

oh sorry

Answer 20

would i take -h out and have 4x + 2h - 11?

Answer 21

oh, you are correct

Answer 22

no need to take - out, just h

Answer 23

okay i was confused for a second

Answer 24

cancel out, and get -4x -2h +11. Now take lim when h --> 0 we have -4x +11 , replace x =9. Dat sit

Answer 25

-25

Answer 26

yup

Answer 27

that should be it! I get it better now! Thank you very very much!

Answer 28

np