If the function e^{-x}f(x) assumes its minimum in the interval [0, 1] at x = 1/4, which of the following is true ? [JEE Adv 2013 P2]

Correct Answer is : f′(x) < f(x), 0 < x < 14

Application of Derivatives

Paragraph for Next 2 Questions
Let f : [0, 1] → R (the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0) = f(1) = 0 and satisfies f′′(x) - 2f′(x) + f(x) ≥ e‌x, x ∈ [0, 1].

Section: Mathematics

Question : 20 of 32

Marks: +1, -0

If the function e‌−xf(x) assumes its minimum in the interval [0, 1] at x =

, which of the following is true ?

[JEE Adv 2013 P2]

f′(x) < f(x),
1
4
< x <
3
4
f′(x) > f(x), 0 < x <
1
4
f′(x) < f(x), 0 < x <
1
4
f′(x) < f(x),
3
4
< x < 1

Validate

Go to Question:

Prev Question

Next Question