Question

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Answer 1

solve for the derivative f '(x) = 0

there it may change inc/dec or dec/inc

Answer 2

test each one to see if the sign changes from one side of tht point to the other

Answer 3

ok what I first did was find the first and second derivatives
-4x^3+4x
2nd -12x^2+4

Answer 4

Good. Label these derivatives.
Find the three values of x that make the first derivative = to 0.
Check each in the 2nd derivative. If the result is concave upward, that's where the graph changes from decreasing to increasing.

Answer 5

You find the x-coordinates of the critical points by finding the 1st derivative.
You use the 2nd derivative to determine whether your curve is concave up (which signifies a minimum at that x value) or down (which signifies a max).
Questions?

Answer 6

−4x^3+4x=0
x= 0,1,-1

Answer 7

when I evaluate the second derivative at each of those critical values I got 0 tho

Answer 8

If your second derivative is 0, that means the 2nd derivative test won't work, and that you must rely on some other method to determine how your graph is behaving.

Answer 9

I dont get it

Answer 10

google (-x^4 + 2x^2)

Answer 11

inc / dec , is all they want, maximum or minimum will change from one to the other

Answer 12

local max/min

Answer 13

can you find the derivative of -x^4 = 2x^2 ?

Answer 14

just test an x on eithe rside of the critical value, see if it changes in the first derivative

Answer 15

f'(x) will change sign - to + at a min or + to - at a max

Answer 16

oh sorry you have already

Answer 17

Other Critical Points:

If f'(x) is undefined, and f(x) is defined.
(Saying some point where f is not differentiable)

Interval boundaries are given, then closed (the included) boundaries are also critical points.

But, respectively, it is a polynomial, and no interval is given, so these two cases don't apply, but good to know for this kind of problems in general.

Answer 18

the second derivative about the concavirty, shows inflections

Answer 19

test a value in each interval , defined by those crit values

Answer 20

increasing - decreasing - increasing - decreasing

name the intervals they want, where it changes from decreasing tp increasing

Answer 21

general shape, for those intervals gives