Question

How do I find the derivative of y=4x-3x^2 at point (2,-4)?

Answer 1

your going to have to use the rather basic power rule for derivatives

Answer 2

\[\frac d{dx}(x^n)=n~x^{(n-1)}\]

Answer 3

How do I solve this by applying the lim/h->0 (f(a+h)-f(a))/h formula?

Answer 4

with lamenting ...

Answer 5

I've attempted this problem a lot, and can't figure out how to use the formula to find the an of -8x+12

Answer 6

*answer

Answer 7

just replace x with a, then replace x with (a+h) and the algebra tends to take care of itself

Answer 8

and a in this case will be 2 correct?

Answer 9

a is just a generic filler

Answer 10

\[\frac{4(a+h)-3(a+h)^2)-(4a-3a^2)}{h}\]

Answer 11

in the end, you would fill in the remaining as with 2 yes

Answer 12

of course I see no reason why you couldnt fill in a at teh start ... just habit i spose :)

Answer 13

@Icecicales do you know what this formula means? \[\lim_{h \rightarrow 0}\frac{ f(x+h)-f(x) }{ h }\]

It is the same thing as this formula you had in algebra to find the slope, but "calculus" \[\frac{ rise }{ run }=\frac{ y _{1}-y _{2} }{ x _{1}-x _{2} }\]

Answer 14

OH,ok, let me try that out

Answer 15

I've never been been good with math and I have to have everything broken down in the smallest terms to understand it.

Answer 16

I swapped my variables around, but you actually end up with the same answer since -1/-1=1/1 anyways but don't let that confuse you... lol

Answer 17

or rather, the limit as the distance in the run approaches zero

Answer 18

Ok, I just plugged in everything a that amistre64 sugggested, but got -3h-20

Answer 19

anyways:
\[\frac{(4(a+h)-3(a+h)^2)-(4a-3a^2)}{h}\]
\[\frac{4a+4h-3a^2-6ah-3h^2-4a+3a^2}{h}\]
\[\frac{4h-6ah-3h^2}{h}\]
\[\frac{h(4-6a-3h)}{h}\]
\[4-6a-3h:~h=0\]
\[4-6a:~a=2;-8\]

Answer 20

in essense, the algebra produces and equivalent function to evaluate without the offending zero denominator

Answer 21

Thank you dude!!!!!!!

Answer 22

youre welcome, I hope you found the spot that you were missing :)

Answer 23

Thank you both