Question

Please help with this calculus problem!



For what values of x is the graph of e^-x62 concave downwards. Explain all steps in detail please.

Answer 1

\[e^{-x62} \] or \[e^{-x^{62}} \] or ???

Answer 2

differentiate your function twice (i'm assuming you can differentiate since you're in calculus)
f'' = 3844e^-64x, which is positive for all x, this means that since f''>0 for all real x, the original function f is concave up for all x, therefore it never decreases

Answer 3

The way I wrote it, is the exact way the question wrote it

Answer 4

sorry, by decreases i mean concave downwards

Answer 5

Ok thanks, is that the answer to the question?

Answer 6

assuming your function is f = {e to the power of -62 times x} then yes

Answer 7

So how would it be written as, \[e ^{-x62}\]?

Answer 8

And can you show the steps you took to get the second derivative, I dont know how to find derivatives

Answer 9

Assume your question is \[e^{-x62}\]
First derivative\[d/dx (e^{-x62}) = d/dx (e^{-62x})= d/dx (e^{-62x}) =-62e^{-62x}\]
second derivatives
\[d/dx (-62e^{-62x}) = (-62)(-62)e^{-62x}\]

Answer 10

So after we have the second derivative what do we do?

Answer 11

I think... put second derivative =0 ... Not sure for this case... :(

Answer 12

refer to my answer above ^

Answer 13

Is the second derivative 3844e^-62x?

Answer 14

K thanks anyway callisto :) I really appreciate it

Answer 15

Is the second derivative 3844e^-62x? -> yes