Mathematics : Application of Derivatives

The interval in which y = x²e^–x is increasing is

• (– ∞, ∞)
• (– 2,  0)
• (2, ∞)
• (2, ∞)

Find the maximum and the minimum values, if there be any, of f given by f(x) = 9x² – 6x + 1, x ∊ R.

Find the maximum and the minimum values, if there be any, of f given by f(x) = x,  x ∊ (0, 1).

Without using derivatives, find the maximum or minimum value of the function 9x² + 12x + 2.

Find the maximum and minimum values, if any, of the following function without using the derivatives:
9x² – 12x + 4

Find the maximum and minimum values, if any, of the following function without using the derivatives:
 4x ² + 28x + 49

Find the maximum and minimum values, if any, of the following function without using the derivatives:
x + 1, x ∊ (– 1, 1)

Find the maximum and minimum values, if any, of the following functions without using the derivatives:
x² 

Find the maximum and minimum values, if any, of the following functions without using the derivatives:
 – (x – 2 )² + 4