Question

Calculus. Please help me and I will give you medals.

Answer 1

@loser can you help me?

Answer 2

@mathmale @freckles

Answer 3

i used the calculator and got it, is that all you need to know is how to type it in

Answer 4

but that's at the second derivative. They gave me the original function. Then I need to derive it to cancel the integral and then I need to drive it again to find the second derivative, but I need help on the limits of this function. How do would you plug the limits after you derive the integral?

Answer 5

derive*

Answer 6

I got sec(4x^2)*8x as the second derivative, but it doesn't give me any of the values.

Answer 7

I know you can just plug it in the calculator, but I need to know how to get the answer

Answer 8

what did you get for F'(x)?

Answer 9

hint use fundamental theorem of calculus

Answer 10

F ' (x) = 2*tan(4x^2)

Answer 11

I got, tan(4x^2)

Answer 12

how did you get the 2?

Answer 13

and you didn't find the derivative of the limit there...
\[F(x)=\int\limits_0^{a(x)}g(t) dt \\ F(x)=G(t)|_0^{a(x)} \\ \text{ assume } G'=g \\ F(x)=G(a(x))-G(0) \\ \text{ differentiate both sides }\]

Answer 14

I used chain rule for the first term
and constant rule for the second term

Answer 15

\[
F'(x)=[G(a(x))]'-[G(0)]' \\ F'(x)=a'(x)G'(a(x))-0 \\ F'(x)=a'(x)g(a(x))\]

Answer 16

okay I see. I forgot the chain rule.

Answer 17

oh isee, calc for the decimal approx answer, i figured just type the thing into a computer algebra system and hit enter.. hah

Answer 18

i know it, but I forgot to apply it

Answer 19

so @DanJS has actually given you the correct F'
and now F'' should be easy to find

Answer 20

i got sec^2(4x^2)*16x

Answer 21

oh and actually your earlier F'' @Joseluess was almost there
you just needed a multiple of 2 there
so great job

and this F'' is like totally right now

Answer 22

you will definitely get one of the answers after plugging in 1

Answer 23

make sure your calc is in radians

Answer 24

16.078 and yes it is. Thank you

Answer 25

no no

Answer 26

your calc is in degrees

Answer 27

put in radians
you can do this by choosing mode

Answer 28

wait, it is in degrees

Answer 29

37.44

Answer 30

cool stuff

Answer 31

yeah radians is like 37.4

Answer 32

is that correct?

Answer 33

yep you are right
I got like 37.4488blahblah

Answer 34

haha thanks both of you goys.