SOLUTION: For what values of x is the function f(x)= 5+15x+6x^2-x^3 decreasing?

Question 262269: For what values of x is the function f(x)= 5+15x+6x^2-x^3 decreasing?
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
here is the problem:
(i)
to determine increasing and decreasing, take a second derivative as
(ii)
set = 0 and find x. We get
(iii)
divide by -3 to get
(iv)
(v)
so, x = -1 and x = 5.
these are critical values.
From (ii) take a second derivative as
(vi) f''(x) =
and solving for x, we get

this is also a critical value.
pick a number less than and greater than 2 in to f'' and we get
x= 0 - - > increasing ; x = 4 - - > decreasing.
--
so the intervals of increasing and decreasing are
increasing (-00, 2)
decreasing (2, +00)
here is the graph to help.

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