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Show that the Function F(X) = 4xcube3 - 18xsquare2 + 27x - 7 Is Always Increasing On R. - CBSE (Commerce) Class 12 - Mathematics

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Question

Show that the function f(x) = 4x3 - 18x2 + 27x - 7 is always increasing on R.

Solution

The given function is:

f(x) = 4x3 - 18x2 + 27x - 7 

On differentiating both sides with respect to x, we get

f'(x) = 12x2 - 36x + 27

⇒f'(x) = 3(4x2 - 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.
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