How do you find the critical numbers for #9x^3 - 25x^2# to determine the maximum and minimum?

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Answer 1 · 2018-03-10T22:23:48

#x=0# & #x=50/27#

Critical points = Where the derivative equals zero

If #f(x)=9x^3-25x^2#

then #f'(x)=27x^2-50x# by the Power Rule

Equate it to zero: #27x^2-50x=0#

This is a quadratic equation with #c=0# so if we divide #x# from both sides we get:

#x(27x-50)=0#

#27x-50=0# Don't forget! Since we divided by #x#, #x=0# is also a critical point.

Add #50# to both sides.

#27x=50#

Divide by #27# from both sides.

#x=50/27#