AP Calculus AB FINAL Review (Semester 2)

what is the average rate of change of the function f(x)=x²-6x+6 from 2 to 6?

• 4

• 2

• 3

• 23/4

What are the conditions that satisfy the mean value theorem, and what does it mean?

• Continuous on the open and differentiable on the closed, and then there is at least 2 numbers c and d in the interval (a,b) (that is a < c < b) such that

• Discontinuous on the closed and differentiable on the open, then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

• Continuous on the closed and differentiable on the open,and then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

• Continuous on the open and differentiable on the open, and then there is no number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

Find the volume of a solid generated by the graph bounded by y=x² and the line y =9 when it is revolved around the x-axis

• 456

• 610.73

• 194.4

• 610.726

A particle moves along the x-axis with velocity at time x>0 and the function is v(x)=x²+6x+3, is the speed of the particle increasing at x=4?

• No because both velocity and acceleration at x=4 is positive

• Yes because both velocity and acceleration at x=4 is positive

• No because both velocity and acceleration at x=4 is negative

• Yes because both velocity and acceleration at x=5 is positive

Alec consumes beverages at a rate of r(x)=10+.2x² beverages per hour, how many beverages does Alec drink in the first 16 hours?

• 25.068

• 433.067

• 5463.759

• Too many, Alec should seek medical attention

What is the derivative of the function f(x)=∫₁^2x(6e^x)dx

• 6e^2x

• 12e^2x

• 6e^2x-6e^x

• 6e^2x

What is the speed of the position function f(x)=-3x²-6x-6 at x=2

• -18

• 18

• -6

• 6

Which of these is the definition of a derivative?

• $\lim_{h\rightarrow0}\ \frac{f\left(x+h\right)-f\left(x\right)}{h}$

• $\lim_{h\rightarrow0}\ \frac{f\left(h\right)-f\left(x\right)}{h}$

• $\lim_{h\rightarrow0}\ \frac{f\left(x+h\right)+f\left(x\right)}{h}$

• $\lim_{h\rightarrow0}\ \frac{f\left(h\right)+f\left(x\right)}{h}$

Which of these sums up the Mean Value Theorem (MVT)?

• $f'\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$

• $f\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$

• $f\left(c\right)=\frac{f'\left(b\right)-f'\left(a\right)}{b-a}$

• $f'\left(c\right)=\frac{f'\left(b\right)-f'\left(a\right)}{b-a}$

Volume using discs revolving around horizontal line. 

•  $\pi\int_{x=a}^{x=b}\left(top\ -bottom\right)^2dx\ \$  

•  $\pi\int_{x=a}^{x=b}\left(top\ -bottom\right)dx\ \$  

•  $\int_{x=a}^{x=b}\left(top\ -bottom\right)^2dx\ \$  

•  $\int_{x=a}^{x=b}\left(top\ -bottom\right)dx\ \$