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THIS IS a ripoff of JEOPARDY!

THIS IS a ripoff of JEOPARDY!. Increasing/Decreasing (2 min). On which intervals is f ( x ) increasing if f ’( x ) = x 2 – 7 x + 6 ?. Inflection Points (3 min). Find the inflection points of g ( x ) =. x = 0, -2, 2. Optimization (2 min).

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THIS IS a ripoff of JEOPARDY!

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  1. THIS ISa ripoff of JEOPARDY!

  2. Increasing/Decreasing (2 min) On which intervals is f(x) increasing if f ’(x) = x2 – 7x + 6 ?

  3. Inflection Points (3 min) Find the inflection points of g(x) = x = 0, -2, 2

  4. Optimization (2 min) At which x-value does the global minimum occur for the function f(x) = 2x3 – 3x2 – 12x on the interval [-2, 3]? At x = 2.

  5. * 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 mm3in 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 = .)

  6. MVT (2 min) What is the mean value of f(x) = ex on the interval [0, 5]? mean value =

  7. Derivatives(2 min) The graph of a twice-differentiable function fis shown in the figure above. Order the following from least to greatest: f(1), f ’(1), f ”(1) f ”(1) , f(1), f’(1)

  8. If f ”(x) = (x + 4)3(x + 3)2(x – 1), thenwhere does the graph of f have inflection points? Concavity(2 min) At x = -4 and 1

  9. 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.

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