Answer:
a) The increasing intervals would be from -4 to 0 and 4 to infinity. The decreasing interval would just be from negative infinity to -4 and 0 to 4.
b) The local maximum comes at x = 0. The local minimums would be x = -4 and x = 4
c) The inflection points are x= +/-√16/3
Step-by-step explanation:
To find the intervals of increasing and decreasing, we can start by finding the answers to part b, which is to find the local maximums and minimums. We do this by taking the derivatives of the equation.
f(x) = x^4 - 32x^2 + 2
f'(x) = 4x^3 - 64x
Now we take the derivative and solve for zero to find the local max and mins.
f'(x) = 4x^3 - 64x
0 = 4x^3 - 64x
0 = 4x(x + 4)(x - 4)
x = -4 OR x = 4 OR 0
Given the shape of a positive 4th power function function, we know that the first and last would be a minimums and the second would be a maximum.
As for the increasing, we know that a 4th power, positive function starts up and decreases to the local minimum. It also decreases after the local max. The rest of the time it would be increasing.
In order to find the inflection point, we take a derivative of the derivative and then solve for zero.
f'(x) = 4x^3 - 64x
f''(x) = 12x^2 - 64
0 = 12x^2 - 64
64 = 12x^2
16/3 = x^2
+/- √16/3 = x
-3/2 = x
Answer:
90°-33°=57°
57=2x+1
-1. -1
56=2x divide both sides by 2
28=x
x =28
Answer:
10oz
Step-by-step explanation:
Solve
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x=10</h2><h2>
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Answer:
-7n =12
n=5
Step-by-step explanation:
You said increased so that makes me think you are talking about multiplying so you would write it as -7n =12 :)
If correct, can you please mark me brainliest:)
