THIS IS

a ripoff of

JEOPARDY!

Increasing/Decreasing (2 min)

On which intervals is f(x) increasing if f ’(x) = x2 – 7x + 6 ?

Inflection Points (3 min)

Find the inflection points of g(x) =

x = 0, -2, 2

Optimization (2 min)

At which x-value does the global minimum occur for the function

f(x) = 2x3 – 3x2 – 12xon the interval [-2, 3]?

At x = 2.

Related Rates (7 min)

A spherical droplet of water is evaporating. Assume that it evaporates from the surface of the sphere in such a

way that the sphere is shrinking from the outside in, but always maintaining a spherical shape. If, at the moment

when the sphere is mm3 in volume, the sphere is shrinking at a rate of mm3/s, find the rate at which the

radius of the sphere is shrinking, using proper units.(Note: the volume of a sphere is given by V = .)

𝑑𝑟𝑑𝑡

=169𝑚𝑚 /𝑠

*

MVT (2 min)

What is the mean value of f(x) = ex on the interval [0, 5]?

mean value =

Derivatives (2 min)

The graph of a twice-differentiable function f is shown in the figure above. Order the following from

least to greatest:f(1), f ’(1), f ”(1)

f ”(1) , f(1), f ’(1)

Concavity (2 min)

If f ”(x) = (x + 4)3(x + 3)2(x – 1), then where does the graph of f have inflection points?

At x = -4 and 1

Extrema (2 min)

The position of a particle moving on a line at time t is p(t) = . Between t = 0 and t = 6, at what time is

the particle at the maximum distance?

At t = 4.