Q8 of 45 Page 1

Show that the function f(x) = x3 - 3x2 + 6x - 100 is increasing on R.

We have-

f(x) = x3 - 3x2 + 6x - 100


⇒ f'(x) = 3x2 - 6x + 6


⇒ f'(x) = 3(x2 - 2x + 2)


⇒ f'(x) = 3[(x-1)2 + 1] ≥ 0 for all x ∈ R


So, f(x) is increasing function for all x ∈ R.


More from this chapter

All 45 →
6

Find the value of c in Rolle’s theorem for the function f(x) = x3 – 3x in

7

The volume of a cube is increasing at the rate of 9 cm3/s. How fast is its surface area increasing when the length of an edge is 10 cm?

 9

The x-coordiante of a point on the line joining the points

P(2, 2, 1) and Q(5,1,-2) is 4. Find its z-coordiante.

 10

A die, whose faces are marked 1, 2, 3, in red and 4, 5, 6 in green, is tossed. Let A be the event “number obtained is even” and B be the event “number obtained is red”. Find if A and B are independent events.