Exams › JEE Advanced › Maths

If the function e^(f(x)) assumes its minimum in the interval [0,1] at x = 1/4, which of the following is true?

1. f'(x) < f(x), 1/4 < x < 3/4
2. f'(x) > f(x), 0 < x < 1/4
3. f'(x) < f(x), 0 < x < 1/4
4. f'(x) > f(x), 3/4 < x < 1

Correct answer: f'(x) < f(x), 0 < x < 1/4

Solution

The function e^(f(x)) assumes its minimum at x = 1/4, which means that for values of x less than 1/4, the derivative of the function f'(x) is less than the function f(x) itself, indicating a specific relationship between the function and its derivative in this interval.

Related JEE Advanced Maths questions

• What is the proportion between the height of the cone with the largest possible volume that can fit inside a sphere and the sphere's diameter?
• Identify the point on the curve 9y² = x³ where the normal to the curve intersects the coordinate axes at equal distances.
• The normal to the parametric curve defined by x = a(cos θ + sin θ) and y = a(sin θ − cos θ) at any given value of θ:
• How many critical points exist for the function y = f(x) within the interval x ∈ [0, 2], if the function satisfies d²y/dx² = 6x - 4 and has a local minimum value of 5 at x = 1?
• What is the absolute minimum value of y = f(x) on the interval x ∈ [0, 2], given that f(x) satisfies the equation d²y/dx² = 6x - 4 and has a local minimum value of 5 at x = 1?
• The function f(x) = 2 |x| + |x+2| - ||x+2|-2| - |2|x|| has a local minimum or a local maximum at x =

⚔️ Practice JEE Advanced Maths free + battle 1v1 →