Calculus I, Fall 2014

Quiz 3

Nov 06, 2014 Show all details.

1. State the Mean Value Theorem. Need not prove it.

2. Let f(x) = x^{2/3}(3 − x). Find absolute max and min of f on [−3, 3].

3. True or False? Explain.

| cos x − 1| ≤ |x| for all values of x.

4. Show that e^{x} ≥ 1 + x + x^{2}/2 on x ≥ 0.

5. Sketch the graph of f(x) = x^{4} − 4x^{3} + 10. Indicate all critical points and points of inflection, if any.

Calculus I, Fall 2014

Quiz 3

Nov 06, 2014 Show all details.

1. State the Mean Value Theorem. Need not prove it.

2. Let f(x) = x^{2/3}(3 − x). Find absolute max and min of f on [−3, 3].

3. True or False? Explain.

| cos x − 1| ≤ |x| for all values of x.

4. Show that e^{x} ≥ 1 + x + x^{2}/2 on x ≥ 0.

5. Sketch the graph of f(x) = x^{4} − 4x^{3} + 10. Indicate all critical points and points of inflection, if any.