Question

What would the second derivative of the attached graph look like?

Answer 1

would it be some kind of a parabola?

Answer 2

please explain! thanks:)

Answer 3

1st derivative is the line tangent to the function, the second derivative would be the line tangent to the line tangent to the function.
not sure the what the term is ..

Answer 4

so would it be like this?

Answer 5

Probably the second one.

Answer 6

ohh okay cool! so normally, the second derivative will be some sort of line?

Answer 7

It's an x^4 graph, 2nd derivative will be and x^2 form

Answer 8

well if you had something like
f(x) = x^3
f'(x) = 3x^2
f''(x) = 6x

Answer 9

@agent0smith what does that mean? x^2 ? :/

Answer 10

oh, it's an x^4 graph, didn't know that lol.
f(x) = x^4
f'(x) = 4x^3
f''(x) = 12x^2

Answer 11

Remember any form of y=x^4 has a derivative y'= 4x^3, which has derivative y''= 12x^2

Answer 12

ohh.. and x^2 is a line? :/

Answer 13

or a parabola then?

Answer 14

x^2 is not a line, i think you know what x^2 is, you said it earlier in the question :P

I would draw the first derivative graph first. then draw the second derivative.

Answer 15

hhaa parabola?

if so , how can i tell if it's concave up or down?

Answer 16

Well it's a positive x^4. Which would have a positive 4x^3 and a positive 12x^2

Answer 17

a concave up parabola?

Answer 18

Yeah, but i think it'd be easiest to draw the first derivative, then use THAT to draw the 2nd.

Answer 19

ahh okay, so it would look something like this?