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2 years ago

13

At what value(s) of x does f(x) = -x^4 + 2x^2 have a relative maximum? (4 points)

1 answer:

Brums [2.3K]2 years ago

3 0

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

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Olenka [21]

Hey there!

<em>With negatives ( $-$ ) you have to switch your symbol to the other way</em>
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Firstly, substitute the $\bold{y\ value }$ as an invisible 1
So, now we have to flip the equation around
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We have to $\bold{multiply}$ by $\bold{-2}$ on each of your sides
$\bold{-2\times\frac{-1}{2}\leq-2\times5}$
$\bold{Cancel \ out:2\times\frac{-1}{2}y \ because \ it \ equal \ 1}$
$\bold{Keep: -2\times5 \ because \ it \ helps \ us \ find \ our \ answer}$
$\bold{-2\times5=-10}$
$\boxed{\boxed{\bold{Answer:y\geq-10}}}\checkmark$

Good luck on your assignment and enjoy your day!

~ $\frak{LoveYourselfFirst:)}$

<em />

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