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another math problem?
Given the following function, f(x)=x^3-6x^2+15, on the interval [-2.5, 5]
A. Determine the open interval(s) where f(x) is increasing.
B. Determine the open interval(s) where f(x) is decreasing.
C. Determine the extreme points and classify them as relative and/or absolute maximum(s) or minimum(s)
Thanks!
1 Answer
- mohanrao dLv 71 decade agoFavorite Answer
f(x) = x^3 - 6x^2 + 15
f ' (x) = 3x^2 - 12x
equate f ' (x) to zero to get critical points
3x^2 - 12x = 0
=> x(x - 4) = 0
x = 0 and 4
f(-2.5) = -125/8 - 6(25/4) + 15 = (120 - 125 - 300)/8 = -305/8 = -38.125
f(0) = 15
f(4) = 64 - 96 + 15 = -17
f(5) = 125 - 150 + 15 = -10
relative minimum is -38.125 and occurs at end point x = -2.5
relative maximum is 15 and occurs at critical points x = 0
C)
now you can classify extreme points.
