Question

FTC part 2 problem

Answer 1

\[g(x)=\int\limits_{0}^{x}t^3e^tdt\]

Answer 2

find \[g "(1)\]

Answer 3

Alright, so take the first derivative, what do you get?

Answer 4

Recall that
\[\large\frac{d}{dx}\int_c^{f(x)}h(t)~dt=h(f(x))\cdot f'(x)\]

Answer 5

\[g ' (x)=3x^6((e^x)^2)+(e^xx^3)^2\]

Answer 6

No, not quite... in this case, \(f(x)=x\) and \(h(t)=t^3e^t\), so
\[h(f(x))=x^3e^x\\
f'(x)=1\]
So
\[g'(x)=x^3e^x\]

Answer 7

So what's the second derivative?

Answer 8

sorry, I was looking at my classnotes. I did my other problems in correctly as well. I was writing myself a note to go back and redo them...

Answer 9

ok second derivate requires product rule

Answer 10

Right, then you evaluate and you're done

Answer 11

\[g " (x)=3x^2e^x+e^xx^3\]

Answer 12

so it 4e ok thanks.....

Answer 13

Yes, you're welcome!