Question

If f(2)=6, f'(2)=-4, and f"(2)=2, what is (d^2*(f^3 (x)))/(dx^2 ) at x=2?

Answer 1

\[\frac{d^2([f(x)]^3)}{dx^2}\]
\[=\frac{d}{dx}(3[f(x)]^2f'(x))=3[2f(x)f'(x)f'(x)+[f(x)]^2f''(x)]\]

Answer 2

\[3[f(2)f'(2)f'(2)+[f(2)]^2f''(2)]\]

Answer 3

now plug in and evaluate and simplify

Answer 4

Thank you I'm going to try it now.

Answer 5

I used chain rule and product rule by the way

Answer 6

okay :)

Answer 7

The answers I keep coming up don't seem correct. Can you please explain in more detail.

Answer 8

lol and I didn't notice you were having problems with this money sorry

Answer 9

just like a woman, they state their opinions and then yougotta live with em ;)

Answer 10

\[3[6(-4)(-4)+(6)^2(2)]=3[6(16)+36(2)]=3[96+72]=3[168]\]

Answer 11

= 504 is what I'm getting

Answer 12

ipso facto

Answer 13

I was missing the 2 in front of the f(x). But I understand now.

Answer 14

i dont think id of come to that today;

Answer 15

lol poor amistre
do you ever come to it? ;)

Answer 16

The radius of a sphere is increasing at a constant rate of 2cm/sec. At the instant when the volume of the sphere is 36π cm^3, what is the rate that the surface area is increasing? Surface area=4π r^2 Volume=4/3π r^3 This one I need a full full explanation on

Answer 17

\[V(t)=\frac{4}{3} \pi [r(t)]^3=> V'(t)=\frac{4}{3} \pi 3 [r(t)]^2 r'(t)\]

Answer 18

\[\S(t)=4 \pi [r(t)]^2 => \S'(t)=4 \pi 2r(t) r'(t)=8 \pi r(t)r'(t)\]

Answer 19

\[V'(t)=4 [r(t)]^2 r'(t)\]

Answer 20

so r'=2 do you see that in the first sentence?

Answer 21

\[V=36 \pi\] from second sentence

Answer 22

we want to know S' based on second sentence

Answer 23

\[36=\frac{4}{3} \pi r^3\]
solve this for r

Answer 24

to find S' this is the only thing we need since r' is already given

Answer 25

oops the V=36 pi

Answer 26

\[36 \pi =\frac{4}{3} \pi r^3\] *

Answer 27

solve that for r

Answer 28

So am I suppose to divide both sides by 4/3\[\pi\] ?

Answer 29

or multiply both sides by 3/(4pi)

Answer 30

so would I have 27pi=r^3?

Answer 31

well the pi's would cancel

Answer 32

27=r^3?

Answer 33

yes since pi/pi=1

so r=3

Answer 34

\[\S'=8 \pi r r'\]

Answer 35

and remember r'=2

Answer 36

So now you can find S'

Answer 37

So I should come up with 48pi cm^2/sec correct?

Answer 38

48 pi is right!

Answer 39

Thanks!!