Home / AP Calculus AB: 2.1 Defining Average and Instantaneous Rates of Change at a Point – Exam Style questions with Answer- MCQ

AP Calculus AB: 2.1 Defining Average and Instantaneous Rates of Change at a Point – Exam Style questions with Answer- MCQ

Question

For time t1, the position of a particle moving along the x-axis is given by \(p(t)=\sqrt{t}-2\),At what time t in the interval \(1\leq t\leq 16\) is the instantaneous velocity of the particle equal to the average velocity of the particle over the interval  \(1\leq t\leq 16\)?

A 1

B \(\frac{121}{25}\)

C \(\frac{25}{4}\)

D 25

▶️Answer/Explanation

Ans:C

Question

If f is the function given by \(f(x)=3x^{2}-x^{3}\),then the average rate of change of on the closed interval [1, 5 ] is

A -21

B -13

C -12

D -9

▶️Answer/Explanation

Ans:B

Question

What is the average rate of change of y = cos (2x) on the interval \(\left [ 0,\frac{\pi }{2} \right ]\)

A \(-\frac{4}{\pi } \)

B -1

C 0

D\(\frac{\sqrt{2}}{2} \)

E\(\frac{4}{\pi }\)

▶️Answer/Explanation

 Ans:A

Question

What is the average rate of change of the function f given by \(f(x)=x^{4}-5x\) on the closed interval [0, 3]?

A 8.5

B 8.7

C 22

D 33

E 66

▶️Answer/Explanation

Ans:C

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