Question

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?

Answer 1