Question

How do i find the inflection points and concavity in this function? f(x)= x^(2) * e^(10x)

Answer 1

find 2nd derivative
inflection point occurs when f''(x) = 0

if f''(x) > 0 , its concave up
if f''(x) < 0 , its concave down

Answer 2

to find derivative use product rule and chain rule
\[f'(x) = 2xe^{10x} + 10x^{2}e^{10x}\]
\[f''(x) = 2e^{10x}+40xe^{10x}+100x^{2}e^{10x}\]

Answer 3

can you take it from here

Answer 4

I cant seem to find the critical points then, when i factor out \[2e ^{10x}\].
I get : \[2e^{10x}(50x ^{2}+20x+1)\]
Would it not exist then?