#### Question

Show that the function f(x) = 4x^{3} - 18x^{2} + 27x - 7 is always increasing on R.

#### Solution

The given function is:

f(x) = 4x^{3} - 18x^{2} + 27x - 7

On differentiating both sides with respect to *x*, we get

f'(x) = 12x^{2} - 36x + 27

⇒f'(x) = 3(4x^{2} - 12x + 9)

⇒f'(x) = 3(2x - 3)^{2}

which is always positive for all *x* ∈ R.

Since, f'(x) ≥ 0 ∀ x ∈ R,

Therefore, f(x) is always increasing on R

Is there an error in this question or solution?

Solution Show that the Function F(X) = 4xcube3 - 18xsquare2 + 27x - 7 Is Always Increasing On R. Concept: Increasing and Decreasing Functions.