Mean Value Theorem Visualizer – AP Calculus AB

1. The MVT requires f to be:

Differentiable on [a, b] Continuous on [a, b] and differentiable on (a, b) Increasing on [a, b] Concave up on [a, b]

2. For f(x) = x² on [0, 4], the value of c guaranteed by MVT is:

c = 1 c = 2 c = 3 c = 4

3. Geometrically, MVT guarantees a tangent line that is:

Perpendicular to the secant Parallel to the secant through endpoints Horizontal Tangent to the x-axis