Question

The function f(x)=2log(x−2)−x2+4x+1increases in the interval.(a)(1,2)(b)(2,3)(c)(5/2,3)(d)(2,4)

Answer 1

$f(x) = 2 log((x - 2)) - {x}^{2} + 4x + 1 \\ diff \\ f {}^{1} x = \frac{2}{x - 2} - 2x + 4 = 0 \\ \frac{2}{x - 2} = 4 - 2x \\ 2 = 2(2 - x)(x - 2) \\ (x - 2)(x - 2) = - 1 \\ {x}^{2} - 4 = - 1 \\ {x}^{2} = 3 \\ x = + \sqrt{3} \: \: and \: - \sqrt{3}$
now check the nature of function before and after +√3 and -√3.... and relate with intervals....



mark as brainliest if helped