1.Let f(x) = 1/4x^4 -8x^2

a. Find the critical values of f(x)

b. Find the intervals over which f(x) is increasing and decreasing

c. using the First Derivative Test, classify the critical values you found in (a) as local maxima, local minima, or neither. Explain your reasoning.

d. Use the Second Derivative Test to classify the critical values you found in part (a) (again).

2. Evaluate the derivatives below

(a) d/dx [cos (/7x^2 +4x^2)]

b. d/dx [x^2cos(x) / x^3 +4x^2]

3. Evaluate the derivative below

a. d/dx [sin (cos(x^2))]

b. d/dx [ x^2 / cos(x) (x^3 - 4x)]

4. Let f(x) = x^3 +6x^2 - 36x + 5

a. Find the critical values of f(x)

b. Find the intervals over which f(x) is decreasing and increasing

c. using the First Derivative Test, classify the critical values you found in (a) as local maxima, local minima, or neither. Explain your reasoning.

d. Use the Second Derivative Test to classify the critical values you found in part (a) (again).