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# Classify each critical point as a relative minimum, maximum, or neither.

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Determine the intervals on which the following functions are increasing and decreasing and classify each of the critical points as a relative minimum, a relative maximum, or neither one.

A) f(x)=3/4x^4+4x^3+6x^2+48

B) g(x)=x^6-6x^5-21x^4

https://brainmass.com/math/optimization/classification-critical-points-511577

#### Solution Preview

(1) f(x) = 3/4x^4 + 4x^3 + 6x^2 + 48
By taking the derivative, f'(x) = 3x^3 + 12x^2 + 12x = 3x(x^2 + 4x + 4) = 3x(x + 2)^2
Setting f'(x) = 0 to get two critical points: x = 0 or x = -2.
Hence, f(x) is increasing when x > 0 ...

#### Solution Summary

In this solution we determine if the following functions are increasing of decreasing and classify each of the critical points as either relative minimum, maximum or neither.

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## Finding Maximum and Minimum Values

Questions:
A) Find all critical points of f(x)=x^5+5x^4-35x^3 and classify each as a relative minimum, relative maximum or neither one.
B) Find the absolute maximum and minimum values of f(x)=2x^4-16x^3-32x^2 on the interval [-3,2].

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