Unit 6 Practice Test

Front

What does it mean if f '(x) > 0 for all x?

Back

The function f is increasing for all values of x.

Front

What does it mean if f ''(x) < 0 for all x?

Back

The function f is concave down for all values of x.

Front

How do you determine the number of relative extrema from a derivative function?

Back

Set the first derivative f '(x) to zero and solve for x. The number of solutions indicates the number of relative extrema.

Front

What is the relationship between velocity and acceleration?

Back

Acceleration is the derivative of velocity with respect to time.

Front

If v(t) = 2t + 3t^3, what is the formula for acceleration a(t)?

Back

a(t) = dv/dt = 2 + 9t^2.

Front

Calculate the acceleration at t = 2 seconds for v(t) = 2t + 3t^3.

Back

a(2) = 2 + 9(2^2) = 38 m/s².

Front

What is the significance of a particle being at the origin?

Back

It indicates the position of the particle is zero on the x-axis.

Front

How do you find the velocity of a particle at a specific time?

Back

Take the derivative of the position function with respect to time.

Front

What does it mean if the velocity of a particle is negative?

Back

The particle is moving in the opposite direction along the x-axis.

Front

What is the first step in solving a problem involving relative extrema?

Back

Identify the critical points by setting the first derivative equal to zero.