second derivative of f(x)=-7x*e^(-3.5*x^2)

Question

anonymous · Answer

Did you find the first derivative yet?

anonymous · Answer

that is the first derivative

anonymous · Answer

should I just do product rule? or chain?

anonymous · Answer

it requires use of the product rule and the chain rule.

anonymous · Answer

Oh, then  you just need to take the derivative once. It is a product, so you will need the product rule. It is also a function composition so you'll need the chain rule also..

anonymous · Answer

ok thank you that's where I got stumped

anonymous · Answer

If the function is a product you will need the product rule.

anonymous · Answer

But if it's a function in a function you need the chain rule, and if it's both, you need both.

anonymous · Answer

$$f'(x)=-7*e ^{7/2* x ^{2}}-7x*(-7x)*e ^{-7/2 *x ^{2}}=...$$
simplify.
can you find the second derivative?

anonymous · Answer

what you wrote is the second derivative that I got but I factored out a -7.

anonymous · Answer

derivative of e^(-7/2 x^2)=-7/2 *2x * e^(...)=-7x*e^(...)

anonymous · Answer

are you Ok now?

anonymous · Answer

yes I am asked to then find where it is concave up or down, so I am setting that second derivative to zero.

anonymous · Answer

right.

anonymous · Answer

it will give you inflection points

anonymous · Answer

i got inflection points:
$$x= \pm 1/\sqrt{7}$$