MonotonicityMedium
Question
Number of solution(s) satistying the equation, 3x2 - 2x3 = log2 (x2 + 1) - log2 x is -
Options
A.1
B.2
C.3
D.none
Solution
3x2 - 2x3 = log2 
, x > 0
f (x) = 3x2 - 2x3
f (x) = 6x - 6x2
= 6x (1 - x)
f (x) ≤ f(1)
f(x) ≤ 1
⇒ LHS ≤ 1&RHS ≥ 1
LHS = RHS = 1 for x = 1
∴ equation has exactly one solution
, x > 0f (x) = 3x2 - 2x3
f (x) = 6x - 6x2
= 6x (1 - x)
f (x) ≤ f(1)
f(x) ≤ 1
⇒ LHS ≤ 1&RHS ≥ 1
LHS = RHS = 1 for x = 1
∴ equation has exactly one solution
Create a free account to view solution
View Solution FreeMore Monotonicity Questions
At x >0, f(x) = is...If for a function f(x), f′(c) > 0 then at x = c, f is-...If f(x) = for −7 ≤ x ≤ 7, then f(x) is increasing function of x in the interval...The function f(x) = cos | x | - 2ax + b increases along the entire number scale. The range of ′a′ is given b...The function f(x) = 2log (x − 2) − x2 + 4x + 1 increases in the interval...