Question

On what interval(s) is the function f(x) = x^3e^(2x) increasing?

Answer 1

guess you have to take the derivative and figure out where it is positive (the derivative that is). did you get the derivative?

Answer 2

\[f'(x)=3x^2e^{2x}+2x^3e^{2x}\]
\[=e^{2x}(3x^2+2x^3)\]

Answer 3

1) (-inf, -3/2], [0,inf)
2) (-inf, -3/2]
3) (-inf, 0], [3/2, inf)
4) (-inf, 3/2]
5) [-3/2, inf)

Answer 4

since
\[e^{2x}>0\] for all x, you job is to look at
\[3x^2+2x^3=x^2(3+2x)\]

Answer 5

and since \[x^2\geq0\] you only need to solve
\[3+2x>0\]
\[3>2x\]
\[\frac{3}{2}>x\]

Answer 6

looks like answer 4

Answer 7

nopee :/

Answer 8

yeah because my algebra stinks
it is
\[3+2x>0\]
\[3>-2x\]
\[-\frac{3}{2}>x\]

Answer 9

lol. i still dont know which interval ;/

Answer 10

maye 1 or 2? idk..