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

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 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 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)

A particle moves along the x-axis with velocity at time x>0 and the function is v(x)=x 2 +6x+3, is the speed of the particle increasing at x=4?

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

No 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+.2x 2 beverages per hour, how many beverages does Alec drink in the first 16 hours?

Too many, Alec should seek medical attention

∑ x y ( x − 1 ) n \sum_x^y\left(x-1\right)^n x ∑ y ( x − 1 ) n Find the function that represents this power series

− 1 < x < 1 -1<x<1 − 1 < x < 1

1 x − 1 \frac{1}{x-1} x − 1 1

1 1 − 2 x \frac{1}{1-2x} 1 − 2 x 1

∑ x y ( x − 1 ) n \sum_x^y\left(x-1\right)^n x ∑ y ( x − 1 ) n Find the interval on x for which the series converges

− 1 < x < 0 -1<x<0 − 1 < x < 0

− 1 < x < 1 -1<x<1 − 1 < x < 1

Which of the following is the Taylor series generated by f(x) at x = π 2 x=\frac{\pi}{2} x = 2 π

∑ 0 ∞ ( − 1 ) n ( x − π 2 ) 2 n ( 2 n ) ! \sum_0^{\infty}\ \left(-1\right)^n\ \frac{\left(x-\frac{\pi}{2}\right)^{2n}}{\left(2n\right)!} 0 ∑ ∞ ( − 1 ) n ( 2 n ) ! ( x − 2 π ) 2 n

\dffdddsum_0^{\infty}\ \left(-1\right)^n\ \frac{\left(x-\frac{\pi}{2}\right)}{\left(2n\right)!} 0 ∑ ∞ ( 2 n ) ! ( x − 2 π )

∑ 0 ∞ ( − 1 ) n ( x − π 2 ) 2 n + 1 ( 2 n ) ! \sum_0^{\infty}\ \left(-1\right)^n\ \frac{\left(x-\frac{\pi}{2}\right)^{2n+1}}{\left(2n\right)!} 0 ∑ ∞ ( − 1 ) n ( 2 n ) ! ( x − 2 π ) 2 n + 1

∑ 0 ∞ ( − 1 ) n ( x − π 2 ) 2 n \sum_0^{\infty}\ \left(-1\right)^n\ \left(x-\frac{\pi}{2}\right)^{2n} 0 ∑ ∞ ( − 1 ) n ( x − 2 π ) 2 n

Review Activity for AP Calculus BC

Authored by Jeffrey Lawson

Mathematics

11th - 12th Grade

CCSS covered

Used 5+ times

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41 questions

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

An ice field is melting at a rate of $M\left(t\right)=4-\left(\sin t\right)^3$ acre-feet per day, where t is measured in days. How many acre-feet of this ice field will melt from the beginning of day 1 (t = 0) to the beginning of day 4 (t = 3)?

10.667

10.951

11.544

11.999

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

A detailed sketch outlining a lawn has the x-axis for one side and the graph of $y=4\sqrt{64-x^2}$ for the outer boundary. If x is measured in feet, what is the projected area of the lawn to the nearest square foot?

1.263

804

402

201

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

The derivative of f is given by $f'\left(x\right)=e^x\left(-x^3+3x\right)-3$ for $0\le x\le5$ . At what value of x is f(x) an absolute minimum?

0.618

1.623

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

The function $f\left(x\right)=\tan3^x$ has one zero in the closed interval [0,1.4]. The derivative at this point is

0.411

1.042

3.451

3.763

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find y' at (-1, 2) if x² - xy + y² = 7.

-3/5

4/5

-2/7

3/7

.

(3x²-2)cos(x³-2x)

-(3x²-2)cos(x³-2x)

cos(2x²-2)

sin(2x²-2)

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

If f(x) = sin³(2x), then f'(x) =

3cos(2x)

3sin(2x)⋅2

3sin²(2x)cos(2x)

3sin²(2x)cos(2x)⋅2

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Review Activity for AP Calculus BC

An ice field is melting at a rate of $M\left(t\right)=4-\left(\sin t\right)^3$ acre-feet per day, where t is measured in days. How many acre-feet of this ice field will melt from the beginning of day 1 (t = 0) to the beginning of day 4 (t = 3)?

A detailed sketch outlining a lawn has the x-axis for one side and the graph of $y=4\sqrt{64-x^2}$ for the outer boundary. If x is measured in feet, what is the projected area of the lawn to the nearest square foot?

The derivative of f is given by $f'\left(x\right)=e^x\left(-x^3+3x\right)-3$ for $0\le x\le5$ . At what value of x is f(x) an absolute minimum?

The function $f\left(x\right)=\tan3^x$ has one zero in the closed interval [0,1.4]. The derivative at this point is

Find y' at (-1, 2) if x² - xy + y² = 7.

.

If f(x) = sin³(2x), then f'(x) =

What is the answer to Problem 1?

What is the answer to Problem 4? (Calculator Active)

Access all questions and much more by creating a free account

Popular Resources on Wayground

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Review Activity for AP Calculus BC

An ice field is melting at a rate of M(t)=4−(sin⁡t)3M\left(t\right)=4-\left(\sin t\right)^3M(t)=4−(sint)3 acre-feet per day, where t is measured in days. How many acre-feet of this ice field will melt from the beginning of day 1 (t = 0) to the beginning of day 4 (t = 3)?

A detailed sketch outlining a lawn has the x-axis for one side and the graph of y=464−x2y=4\sqrt{64-x^2}y=464−x2​ for the outer boundary. If x is measured in feet, what is the projected area of the lawn to the nearest square foot?

The derivative of f is given by f′(x)=ex(−x3+3x)−3f'\left(x\right)=e^x\left(-x^3+3x\right)-3f′(x)=ex(−x3+3x)−3 for 0≤x≤50\le x\le50≤x≤5 . At what value of x is f(x) an absolute minimum?

The function f(x)=tan⁡3xf\left(x\right)=\tan3^xf(x)=tan3x has one zero in the closed interval [0,1.4]. The derivative at this point is

Find y' at (-1, 2) if x2 - xy + y2 = 7.

.

If f(x) = sin3(2x), then f'(x) =

What is the answer to Problem 1?

What is the answer to Problem 4? (Calculator Active)

Access all questions and much more by creating a free account

Popular Resources on Wayground

Discover more resources for Mathematics

An ice field is melting at a rate of $M\left(t\right)=4-\left(\sin t\right)^3$ acre-feet per day, where t is measured in days. How many acre-feet of this ice field will melt from the beginning of day 1 (t = 0) to the beginning of day 4 (t = 3)?

A detailed sketch outlining a lawn has the x-axis for one side and the graph of $y=4\sqrt{64-x^2}$ for the outer boundary. If x is measured in feet, what is the projected area of the lawn to the nearest square foot?

The derivative of f is given by $f'\left(x\right)=e^x\left(-x^3+3x\right)-3$ for $0\le x\le5$ . At what value of x is f(x) an absolute minimum?

The function $f\left(x\right)=\tan3^x$ has one zero in the closed interval [0,1.4]. The derivative at this point is

Find y' at (-1, 2) if x² - xy + y² = 7.

If f(x) = sin³(2x), then f'(x) =