First Derivative Test
Concavity/Inflection
Second Derivative Test
100
Find the local extreme value(s) of y=x^2-8x
There is a local minimum at x=4
100
The graph of f(x) is concave up when f" _______, meaning f'(x) is______.
The graph of f(x) is concave up when f"(x)>0, meaning f'(x) is increasing
100
Using the second derivative test, determine the local extreme values of y=2x^3-24x-5
The graph has a local max at x=-2 and a local min at x=2
200
The equation y=x^3+3x is on the interval (0, 1). Is there a local maximum or minimum at x=1? (Explain why)
Local max at x=1 because y'>0 @ right endpoint b
200
Find where y=sin(3x) is concave up and concave down on the interval (0, 2pi/3)
y=sin(3x) is concave down on the interval (0, pi/3) and concave up on the interval (pi/3, 2pi/3)
200
Use the second derivative test to find the extrema for the function y=3x^5-25x^3+60x+20
There is a local maximum at x=-2 and a local minimum at x=-1
300
Find the local extrema of the equation y=x^4-8x^2+2
The local minima occur at x=-2 and x=2. The local maximum occurs at x=0.
300
Find the points of inflection of y=x^4-2x^3-6x
There is a point of inflection at x=0 and x=1.
300
Use the second derivative test to find the local extrema of the function y=xe^(2x)
There is a local minimum at x=-1/2
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