Question

determine the intervals over which the function is increasing
y=2x^3+3x^2-12x

Answer 1

Can you take the derivative??

Answer 2

Take the derivative and put that is equal to 0..

Answer 3

didnt learn about derivatives yet :(

Answer 4

:) then, compute
\[\frac{f(x)-f(y)}{x-y}\]
and see where It's positive or negative !

Answer 5

\[
f(x)=2 x^3+3 x^2-12 x\\
f'(x)=-12 + 6 x + 6 x^2=\\
6 (-1 + x) (2 + x)\\
f'(x) >0 \text { when } x < -2 \text { or }
x> 1\\
f'(x) <0 \text { when } -2 < x <1
\]

f is increasing on \( ]-\infty -2[\cup]1, \infty[\)

f is decreasing on \( ]-2, 1[\)