Question

Find the intervals where f is increasing and decreasing and identify its local maxima and minima using derivative tests. Given:

f(x) = 4x^3 + 3x^2 - 6x + 1

Answer 1

start by taking the derivative, set it equal to 0, and solve x
that gives u critical points

Answer 2

yeah, so far I've got.

(4x-2) (3x+3)

and x = 1/2, -1

Answer 3

is that correct or ... ? :)

Answer 4

looks good :)

Answer 5

save those values, we will it for figuring out relative maxima/minima

Answer 6

first lets find out, where f is increasing/decreasing, by looking at the first derivative.

Answer 7

\(\large f'(x) = (4x-2) (3x+3)\)

Answer 8

can u tell me when this function is POSITIVE and when it is NEGATIVE ?

Answer 9

oh okay, trying to solve it :)

Answer 10

easy way is to notice that this function(first derivative) is just a parabola

Answer 11

uhm okay, at this point, im just using the sign analysis, idk but this is what my teacher taught us to do :)

Answer 12

so, it stays NEGATIVE between the x-intercepts. and POSITIVE everywhere else

Answer 13

oh yes! i got the same answers! :D