1. Find the local maximum and minimum values off using both theFirst andSecond Derivative Tests.

f(x) = 1 + 6x² + 4x³

2. Consider the function below. (Use U to denote the union of two intervals.)

f(x) = 2 + 2x² -x⁴

(a) Find the interval(s) of increase and decrease. (Enter your answer using interval notation.)

(b) Find the local minimum and maximum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

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

3. Consider the function below.

f(x) = 6xtanx, -/2 < x < /2

(a) Find the vertical and horizontal asymptote(s).

(b) Find the interval where the function is increasing and decreasing. (Enter your answer using interval notation.)

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

(d) Find the interval where the function is concave up. (Enter your answer using interval notation.)