Question

Consider the function below. (If an answer does not exist, enter DNE.) f(x) = 1/2x^(4) −...

Consider the function below. (If an answer does not exist, enter DNE.)

f(x) = 1/2x^(4) − 4x^(2) + 3

(a)

Find the interval of increase. (Enter your answer using interval notation.)

Find the interval of decrease. (Enter your answer using interval notation.)

(b)

Find the local minimum value(s). (Enter your answers as a comma-separated list.)

Find the local maximum value(s). (Enter your answers as a comma-separated list.)

(c)

Find the inflection points.

(x, y) = (smaller x-value)

(x, y) = (larger x-value)

Find the interval where the graph is concave upward. (Enter your answer using interval notation.)

Find the interval where the graph is concave downward. (Enter your answer using interval notation.)

(d)

Use the information from parts (a)-(c) to sketch the graph. Check your work with a graphing device if you have one.

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