Prove that the function given by f (x) = x3 - 3x2 + 3x - 100 is increasing in R

Solution:

Increasing functions are those functions that increase monotonically within a particular domain,

and decreasing functions are those which decrease monotonically within a particular domain.

We have

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

Therefore,

On differentiating wrt x, we get

f' (x) = 3x2 - 6x + 3

Changing into whole square form

= 3(x2 - 2x + 1)

= 3(x - 1)2

For x ∈ R ,

(x - 1)2 ≠ 0

So, f' (x) is always positive in R.

If f' (x) > 0 then the function is strictly increasing.

Thus,

the function is increasing in R

NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.2 Question 18

Prove that the function given by f (x) = x3 - 3x2 + 3x - 100 is increasing in R

Summary:

Hence we have concluded that the function given by f (x) = x3 - 3x2 + 3x - 100 is increasing in R. If f' (x) > 0 then the function is strictly increasing

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