Mark the correct alternative in the following: The function f(x) = 2log(x – 2) – x 2 + 4x + 1 increases on the interval.

Question

Philoid · Accepted Answer

Formula:- The necessary and sufficient condition for differentiable function defined on (a,b) to be strictly increasing on (a,b) is that f’(x)>0 for all x(a,b)

Given:-

f(x) = 2log(x – 2) – x² + 4x + 1

f^’(x)=

now for increasing

f^’(x)>0

3<0 and x-2>0

and x>2

Mark the correct alternative in the following:The function f(x) = 2log(x – 2) – x2 + 4x + 1 increases on the interval.

Mark the correct alternative in the following:
The function f(x) = 2log(x – 2) – x² + 4x + 1 increases on the interval.