Precalc Final Review Double Jeopardy

Derivative Concepts and Applications

100

What does the derivative of a function represent graphically?

The slope of the tangent line to the graph of the function

200

What does the limit definition of the derivative of f(x) represent graphically?

What is the limit of the average rate of change as the change in x approaches 0?

300

The derivative of a function is positive at some value x = a

What is increasing?

400

f(x) = x^2+2x

Find the equation of the tangent line to the graph at x = 1.

y - 3 = 4(x - 1)

500

A graph of a function shows a curve that is increasing, flattens out, and then decreases. At what point is the derivative likely to be zero, and what does this imply about the function at that point?

What is a turning points ? (relative min/max also acceptable)

Polar

100

What are the rectangular coordinates of the point (2,5π/6) in polar form?

-sqrt(3), 1

200

What are the polar coordinates of the point (0,2) in rectangular form?

(2, π/2)

300

Convert the polar equation r=3sec⁡(θ) to rectangular form

x=3

400

Convert to polar

x^2+y^2=4x

r=4costheta

500

Convert the polar equation r=3cos⁡(θ) to rectangular form

x^2+y^2=3x