Let f (x) = x⁴ – 4x, then
Recall the rule solving fully: apply relevant formula, put numbers, compute. Result comes as f is increasing in [1,∞). Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XI and XII
#function analysis
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The maximum value of (log x)/x is
We know that we verify 1/e by full calculation: use standard identity, substitute, simplify step by step to reach 1/e.
Ref: NCERT Mathematics Class XII — Applications of Derivatives
The minimum value of the function f(x) = |x - 4| exists at
Applying the basic concept, we verify x = 4 by full calculation: use standard identity, substitute, simplify step by step to reach x = 4.
Ref: NCERT Mathematics Class XII — Applications of Derivatives
At how many points is the function f(x) = [x] discontinuous?
Recall the rule we verify Infinite by full calculation: use standard identity, substitute, simplify step by step to reach Infinite.
Ref: NCERT Mathematics Class XI and XII
If f( x ) = array*20c 1 + x&if;x < 0 ( 1 - x )( px + q )&if;x 0 array .
The trick is solving fully: apply relevant formula, put numbers, compute. Result comes as (2, 1). Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XI and XII
The function f(x) is defined by f( x ) = array*20c | x |x 0, arrayarray*20c ,x 0 x = 0 array . then, at x = 0 it is
Let's break it down: solving fully: apply relevant formula, put numbers, compute. Result comes as Discontinuous at x = 0 and has discontinuity of first kind. Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XI and XII
Find the domain of the inverse trigonometric function ^ - 1( 2x 1 - x^2 ) is,
We know that we verify [ - 1 2 ,1 2 ] by full calculation: use standard identity, substitute, simplify step by step to reach [ - 1 2 ,1 2 ].
Ref: NCERT Mathematics Class XI — Sets, Relations and Functions
In (0, π/2), function f(x)=x/1+x x , have
Think of it like this: after simplifying, one maximum point is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XI — Trigonometry
