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.