f(x) = -x(x-3)^2
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We have the function as
Determinig the x intercept ,put f(x)=0
x=0 and x=3
y intercept is put x=0 we get 0
Thus the determined point are (3,0)(0,0)
Also -x(x-3)^2 >0
And -x(x-3)^2 <0
Determining relative the maxima and minima value
Divide with -3 ,we get
x=1 and x=3
Now the second derivative is d(f(X)/dx^2=d(-3x^2-9+12x)/dx=-6x+12
at x=1 d^y/dx^2=6>0 therefore minima occur and the minimum value is -4
at x=3,d^2y/dx^2=-6*3+12 =-6 maxima occur and the maximum value is 3
Using the above information creating a table of values
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