On the interval `[0,1]` the function `f(x) = x^1005 (1 - x)^1002` assumes maximum value equal to

On the interval [0,1] the function phi(x)=x^(1005)(1-x)^(1005) takes its maximum value at point

On the interval [0,1] the function x^(25)(1-x)^(75) takes its maximum value at the point

In the interval [0,1] the function x^(25)(1-x)^(75) takes a maximum value at

On the interval [-(pi)/(4) , (pi)/(4)] , the function f (x) = sqrt(1 + sin^(2) x) has a maximum value of

Let f:[0,1] rarr R be a function.such that f(0)=f(1)=0 and f''(x)+f(x) ge e^x for all x in [0,1] .If the fucntion f(x)e^(-x) assumes its minimum in the interval [0,1] at x=1/4 which of the following is true ?