AP Calculus

What’s inside

• For the function f(x) = x^3 - 6x^2 + 9x, on which intervals is f increasing?
• What is the value of lim(x→0) [sin(5x) / x]?
• A particle moves along a line with velocity v(t) = t^2 − 4t + 3 for 0 ≤ t ≤ 4. During which interval is the particle…
• If f′(x) = 2x cos(x^2) and f(0) = 3, what is f(1)?
• The region bounded by y = x and y = x^2 on [0, 1] is revolved about the x-axis. What is its volume?
• At which x-value does the function f(x) = x^4 − 4x^3 have a local maximum?
• Match each derivative expression with its antiderivative.
• Match each theorem or concept with its key condition or conclusion.