AP Calculus to section 3-5 Derivatives and Limits

limit as x → 0 of function shown in graph

Estimate the acceleration of the boat at t = 12.5 minutes

Given graph of f ' (x), on what interval (s) is f (x) decreasing ?

Use the values in the table to find the derivative of f(x) g(x) at x = 3

Find the average acceleration of the boat over the interval [5, 10]

The position of a particle is given by s(t) = 3x² - 7x. Describe its speed at t = 1.

The Product Rule states (ab) ' =

Find the average rate of change of y = x ² on [1 , 3]

Find y ' (2) if y = 1/x

Find an equation of the tangent line to y = x² at x = 3

Find the instantaneous rate of change of y = x ⁴ at x = 2.

limit as x → 1 of function shown in graph

The derivative of (cos x) / 2x at t = π

Find the velocity function if the position function is s(t) = x ⁵ + x ⁴ - 4x

Find the slope of y = x ³ at x = 3

The slopes of parallel lines are

limit as x→3 ⁺ of graph of function

Find the value of x where the tangent line to f(x) = x ² - 4x is horizontal.

Find y ' if y = sin x

Find f ' (x) if f (x) = 3x ⁴ - 5x ² + 8