How do you find the local max and min for #f (x) = x^(3) - 6x^(2) + 5#?
2 Answers
#
Explanation:
Find the critical values (when
Make a sign chart for
There is a relative maximum at
There is a relative minimum at
Look at a graph:
graph{x^3-6x^2+5 [-36.65, 55.83, -32.08, 14.18]}
It has a local maxima at
It has a local minima at
Explanation:
Given -
#y=x^3-6x^2+5#
#dy/dx=3x^2-12x#
#(d^2y)/dx^2=6x-12#
#dy/dx=0 =>3x^2-12x=0#
#3x(x-4)=0#
#3x=0 #
#x=0#
#x-4=0#
#x=4#
AT
At
AT
Local Maximum is -
At
AT
Local Minimum -
At
graph{x^3-6x^2+5 [-58.5, 58.55, -29.24, 29.3]}