Consider the function f(x)=–2x^3+33x^2–60x+4?

Question

For this function there are three important intervals: (–infin, A] , [A,B] , and [B, infin) where A and B are the critical numbers. A=___? B=___?

f(x) has an inflection point at x=C, where C is ___?

Answer 1

A and B are roots of the equation -x^2+11x-10=0. C is the solution to -2x+11=0 or x=-5.5

Answer 2

easy enough
Find the first derivative
which is
6x^2 + 66x -60
get the zeros for that
the zeros of the first derivative will be the
critical points of f(x).
the zeros of the first derivative happen to be
x= -11.84
x = 0.84
Since the question is talking about intervals u don't need the y coordinates for these points.. so this is all you need.

then get the second derivative.
which is
12x + 66
set that = 0 and that will be
the x coordinate of the point of inflection
(-11/2, 1999/2)

Answer 3

I'm guessing that A and B are the local maxima and minima of the function, so take the derivative, set it equal to zero, solve it for x, and those are the values of A and B. To find out which is which, take the 2'nd derivative and evaluate is at x=A and x=B. Where it evaluates to a positive value, you have a local minima and the one which evaluates to a negative value is a local maxima.

To find the inflection point(s) setthe 2'nd derivative equal to zero and solve it for x. This is the point at which the curvature of the function changes from concave to convex.

HTH

Doug

Answer 4

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