Question

# 1) Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval....

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) = 1 − 12x + 2x^2, [2, 4]

c =

2) If f(2) = 7 and f '(x) ≥ 1 for 2 ≤ x ≤ 4, how small can f(4) possibly be?

3) Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?

f(x) = 4x2 − 5x + 3,    [0, 2]

3a) If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisify the hypotheses, enter DNE).

c =

4) Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x) = square root x

c=?, [0,25]

4b) Graph the function, the secant line through the endpoints, and the tangent line at (c, f(c)).

4c) Are the secant line and the tangent line parallel?

Yes or No?

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