For f (x ) = x^3-9x^2, use calculus to determine the location of: a. Any maximum or minimum points (tell which are max and which are min) b. Any inflection points

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a ) f (x ) = x^3-9x^2

f'(x) = 3x ^2 - 18x =0

x= 0 or x = 6

at x = 0,

f (x ) = 0

at x = 6 ,

f(x) = -108

so maximum of f (x ) = x^3- 9x^2 = 0 at x=0.................................ANSWER

minimum of f (x ) = x^3- 9x^2 = -108 at x = 6.......................................ANSWER

b) f'(x) = 3x ^2 - 18x

f''(x)= 6x - 18

6x - 18 = 0

x = 3

inflection point is at x= 3.............................................ANSWER

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