Show that f(x) = x3 - 15x2+75x - 50 is increasing on R. – InterviewSolution

1.

Show that f(x) = x3 - 15x2+75x - 50 is increasing on R.

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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