At what value(s) of x does f(x) = -x^4 + 2x^2 have a relative maximum? (4 points)
1 answer:
Take the derivitive
f'(x)=-4x^3+4x
find where it equals 0
0=-4x(x^2-1)
0=-4x(x-1)(x+1)
at x=-1, 0, 1
those are critical points
put those on number line
test points between to see if positive or negative
f'(-2)=(+)
f'(-0.5)=(-)
f'(0.5)=(+)
f'(2)=(-)
see attachment
remember the max is where the slope changes from positive to negative
at -1 and 1 only
f'(x)=-4x^3+4x
find where it equals 0
0=-4x(x^2-1)
0=-4x(x-1)(x+1)
at x=-1, 0, 1
those are critical points
put those on number line
test points between to see if positive or negative
f'(-2)=(+)
f'(-0.5)=(-)
f'(0.5)=(+)
f'(2)=(-)
see attachment
remember the max is where the slope changes from positive to negative
at -1 and 1 only
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Answer: Choise A and Choise B.
Step-by-step explanation:
Given the following expression:
You can simplify it in order to find equivalent expressions.
Appying the Distributive Property, you get:
So:
1. If you add the like terms, you get this equivalent expression:
2. But if you factor out 3, you get the following equivalent expression:
Therefore, the expression shown in Choice A and Choise B are equivalents to the expression