Answer :

Consider f(x)=x3-15x2+75x-50


Domain of the function is R.


f’(x)=3x2-30x+75


=3(x2-10+25)


=3(x-5) (x-5)


=3(x-5)2


f’(x)=0 for x=5


for x<5


f’(x)>5


and


for x>5


f’(x)>5


we can see throughout R the derivative is +ve but at x=5 it is 0 so it is increasing.


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