Differentiation 1
Differentiation 2
Anti-differentiation
Theorems
Applications
100

What does d/dx mean?

What is the derivative with respects to x?

100

What does dx/dy mean?

What is the derivative of x with respect to y?

100

What can you find from the integral?

What is Anti-derivative, area under the curve, and  approximation

100

Complete the Fundamental Theorem of Calculus. ∫abF(x)dx=?

What is F(b)-F(a)?

100

When finding the area between curves, how do you determine which function is top or bottom?

What is if on the x axis , use distance from X axis.  If Y-axis, use distance from y-axis (rotate graph 90 degrees for better view).

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

Why is it important to incorporate the +C in your anti-derivative?

What is because +C represents any constant which could be included in the original function

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

If a graph of acceleration was given, how would you be able to determine the velocity over a certain interval?

What is by finding the area under the curve/ intergration.

300
Find the slope of f(x)=5/3x3-3x2-1/x2 at x=-1
What is 9?
300
Find dy/dx for the following function: x2y3+y2+3x=y.
What is (-3-2xy3)/(3x2y2+2y-1)?
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

Find a value c such that the conclusion of the mean value theorem is satisfied for f(x)=2x,3+6x-2 on the interval [-2,2].

What is &plusmn 2/(3)^1/2?

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
Find the derivative of f(x)=(x+3)3/(x-2)2-x2(7x+7)
What is (x+3)2[3(x-2)-2(x+3)]/(x-2)3-21x2-14x?
400
Find the derivative of f(x)=tan(3x).
What is 3sec2(3x)
400

Solve for y=f(x) when f(3)=2. dy/dx=x2+3x/y2

What is (2/3x3+2x2-32)1/2?

400

What is the second fundamental theorem of calculus?

What is if f is a continuous function and c is any constant, then A(x)=∫xcf(t)dt is the unique antiderivative of f that satisfies A(c)=0.

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

What does the derivative tell you?

What is the slope at a point and rate of change.

500
Solve for d2y/dx2 when y2=3x2+4x+y at the point (2,5).
What is -.036?
500
Integrate x/(4+x2).5.
What is (4+x2).5+C?
500
Use the second Fundamental Theorem of Calculus to find F'(x). F(x)=∫-3x(7t+9)dt.
What is 7x+9?
500
When would you use the disk/washer method?

What is when finding the volume of the solid generated by revolving the region by the functions F(x) and F(y).

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