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Differentiation 1
Differentiation 2
Anti-differentiation
Theorems
Applications
100
Find the derivative of f(x)=3/2x2
What is 3x?
100
Find dy/dx. xy2+y3+x2=10
What is (-2x-y2)/(2xy+3y2)?
100
Integrate F'(x)=3x2+6x.
What is x3+3x2+C?
100
Complete the Fundamental Theorem of Calculus. ∫abF(x)dx=?
What is F(b)-F(a)?
100
Find the area of the region bounded by f(x)=x2-3x-10 and g(x)=-x2+5x+14.
What is 170.667?
200

Find the derivative of 7x3+9x2+5x

What is 21x2+18x+5?

200
Find the derivative of f(x)=ln(x3+3x2+7).
What is (3x2+6x)/(x3+3x2+7)?
200
Integrate F'(x) = x2
What is (x3/3 +C
200
What does the Mean Value Theorem state?
What is there exists a point c in the interval (a,b) such that f'(c)=f(b)-f(a)/b-a, if a function is continuous on the closed interval [a,b] and differentiable on the open interval (a,b)?
200
Find the average acceleration of a particle over the interval (0,50) given v(50)=80ft/sec and an initial velocity of 10 ft/sec. Include units in your answer.
What is 7/5 ft/sec2?
300

Find the slope of f(x)=5/3x3-3x2-1/x2 at x=-1

What is 9?

300

I'm a line perpendicular to a tangent line. What is my name?

What is a normal line?

300
Find the equation of F given F'(x)=x3-3x2+7x+8 and F(0)=5
What is F(x)=(x4/4)-x3+3.5x2+8x+5
300

What does the Intermediate Value Theorem state?

If f(x) is continuous on [a, b] then f(x) will achieve every y value between f(a) and f(b).

300
The rate of change of radius r of a circle is 4 cm/s. Find the rate of change of Area A when r=2cm.
What is 16π?
400

Name one of the founding fathers of calculus. 

Who is Isaac Newton or Gottfried Leibniz?

400
Find the derivative of f(x)=tan(3x).
What is 3sec2(3x)
400

What characteristic of f(x) would dictate whether or not an LRAM approximation of the area under f(x) would be an overestimate or an underestimate?

What is increasing/decreasing?

400
Use the second Fundamental Theorem of Calculus to find F'(x). F(x)=∫2x(9t+9)dt.
What is 9x+9?
400
The acceleration of a particle is given by the function a(t)=3t2+7. Find the position function of the particle given that its initial velocity is 10 m/sec and an initial height of 80m.
What is s(t)=(t4/4)+3.5t2+10t+80?
500

How would you justify that f(x) has a local minimum at x = a?

First Derivative Test: Show that f'(a) = 0 or f'(a) is undefined and show that f'(x) switches from negative to positive at x = a.

Second Derivative Test: Show that f'(a) = 0 or f'(a) is undefined and f''(a) is positive.

500
Solve for d2y/dx2 when y2=3x2+4x+y at the point (2,5).
What is -.036?
500

What characteristic of f(x) would dictate whether a Trapezoidal approximation of the area under f(x) is an overestimate or an underestimate?

What is concavity?

500

Which theorem allows us to determine the limit of a function by showing that two other limits converge around the wanted limit?

What is the sandwich theorem.

500

Find the volume of the solid generated by revolving the region bounded by y=x2, the x-axis, and x=2 around the x-axis.

What is 32π/5?