What is the critical points of the given function

Reference no: EM131012551

1. Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.)

f(x) = x³ -x² - 12x + 3, [0, 4]

2. Show that the equation has exactly one real root.

x + cos x = 0.

3. Suppose that for 4 ≤ f'(x) ≤ 5 for all values of x. What are the minimum and maximum possible values of f(6) - f(1)?

4. Find the absolute maximum and absolute minimum values of f on the given interval.

f(x) = xe^{-e^2/32}, [-2, 8]

5. Find the critical points of the function. (Enter your answers as a comma-separated list.)

g(x) = √(1 - x²)

Reference no: EM131012551

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