If φ (x) = f (x) + f (2a – x) and f ’’ (x) > 0, a > 0, 0 < x < 2a then

Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability

1. φ (x) increases in [a, 2a]
2. φ (x) increases in [0, a]
3. φ (x) decreases in [0, a]
4. φ (x) decreases in [a, 2a]

Answer

(A) φ (x) increases in [a, 2a], (C) φ (x) decreases in [0, a]

Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.

Related practice questions

• If a _ 1 =1 and a_ n+1 = 4+3 a_ n 3+2 a_ n , n 1 and if _ n a _ n+1 = a, then the value of a is :
• The length of subtangent to the curve x 2 y 2 = a 4 at the point (–a, a) is
• Let f(x)= x a^ 2 +x^ 2 - d-x b^ 2 +(d-x)^ 2 , x F , where a, b and d are non-zero real constants. Then:
• If y= _ u(x) ^ v(x) f(t) d t let us define d y d x in a different manner as d y d x =v^ (x) f^ 2 (v(x))-u^…
• Assertion : Let f : [0, ∞)→[0, ∞) and g : [0, ∞)→[0, ∞) be non-increasing and non-decreasing functions…
• If y=f(x) is a curve and if there exists two points A (x_ 1 , f (x_ 1 ) ) and B (x_ 2 , f (x_ 2 ) ) on it…
• Evaluate, _ x / 4 x- x ( 4 -x )( x+ x) .
• For the parabola y 2 = 4ax, the ratio of the sub-tangent to the abscissa is

More Limit, Continuity and Differentiability questions · Browse all practice questions