Applications of Derivatives Review

Front

What is the maximum area of a rectangular pigpen that can be constructed with 400 ft of fencing next to a wall?

Back

The maximum area is 20000 square feet, achieved with dimensions 100 ft x 200 ft.

Front

How do you find the instantaneous velocity of a particle given its position function s(t)?

Back

You find the instantaneous velocity by taking the first derivative of the position function, v(t) = s'(t).

Front

What is the first derivative of the position function s(t) = -t^2 - t?

Back

The first derivative is v(t) = -2t - 1.

Front

What is the initial position of a particle described by the function x(t) = t^3 - 4t^2 + 7?

Back

The initial position is x(0) = 7.

Front

How do you calculate the acceleration of an object from its position function?

Back

Acceleration is found by taking the second derivative of the position function.

Front

What is the acceleration of the object at time t = 2 s if x(t) = 3t^2 + 5t^3 - 2t?

Back

The acceleration at t = 2 s is 66 m/s².

Front

What does the second derivative of a position function represent?

Back

The second derivative represents the acceleration of the object.

Front

If the position function is s(t) = -t^2 - t, what is the velocity at t = 1?

Back

The velocity at t = 1 is v(1) = -2(1) - 1 = -3.

Front

What is the relationship between position, velocity, and acceleration?

Back

Position is the integral of velocity, and velocity is the integral of acceleration.

Front

What is the formula for the area of a rectangle?

Back

Area = length × width.