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Math · Calculus
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Calc 4.3

1. Find the intervals of concavity and inflection points of the function. (Give your intervals of concavity in interval notation. If an answer does not exist, enter DNE.)

f(x) = x4 − 12x3 + 54x2 − 1

Concave up:

Concave down:

Inflection Point:

2. Find the intervals of concavity and inflection points of the function. (Give your intervals of concavity in interval notation. If an answer does not exist, enter DNE.)

V(x) = x4 + 6x3 − 60x2 + 6

Concave up:

Concave down:

Inflection Point (smaller x value)=

Inflection Point (larger x value)=

3. Consider the following.

f(x) = x3 − 75x + 4

(a) Find the intervals on which f is increasing or decreasing. (Enter your answers using interval notation.)

Increasing:

Decreasing:

(b) Find the local maximum and minimum values of f. (If an answer does not exist, enter DNE.)

Local minimum value:

Local Maximum value

(c) Find the intervals of concavity and the inflection points. (Enter your answers using interval notation.)

Concave up:

Concave down:

Inflection point:

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