Derivative Concepts and Applications
What does the derivative of a function represent graphically?
The slope of the tangent line to the graph of the function
What are the rectangular coordinates of the point (2,5π/6) in polar form?
-sqrt(3), 1
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?
What are the polar coordinates of the point (0,2) in rectangular form?
(2, π/2)
What is increasing?
Convert the polar equation r=3sec(θ) to rectangular form
x=3
f(x) = x^2+2x
Find the equation of the tangent line to the graph at x = 1.
y - 3 = 4(x - 1)
Convert to polar
x^2+y^2=4x
r=4costheta
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)
Convert the polar equation r=3cos(θ) to rectangular form
x^2+y^2=3x