AP Calculus AB Practice Set 5

Consider the graph of a function f as shown below:

F\prime\left(x\right)=\frac{x^3+\cos{x}}{x^2-3}dx

If F(x) is the antiderivative of the function F\prime(x) , then what is the value of F(7) – F(5)?

Consider a continuous function g that is positive and has domain x > 0. If the asymptotes of the graph of g are x = 0 and y = 3, then which of the following is true?

A car’s speed is modeled by the differentiable function g(t), where t is the time in hours since the start of the journey and g(t) is measured in kilometers per hour. Which of the following is the best interpretation of g\prime(3) = 15.2?

The function f has the first derivative given by f\left(x\right)=-x^5+x^4+2x^3-2x^2-x+1 . On what intervals is the graph of f concave up?

Consider the graph of functions f, g, and h above. Which of the following statements is true?

A car moves along a straight road with velocity v(t)=4t^2\cos{(t)} kilometer per hour. Determine the total distance, in kilometers, covered by the car during the time interval 0\le t\le3 hours.

Consider the derivative of a function f:

f^\prime\left(x\right)=\frac{2(x^2-1)}{(x^2+x+1)^2}

At what value of x does the given function achieve a relative minimum?