The maximum and minimum value of 3x⁴-8x³+12x²-48x+1  on the interval [1,4] is

Let f (x) satisfy the requirements of Lagrange's Mean Value Theorem in [0, 2].If f (0) = 0 and | f' (x) | ≤ 1/2 for all x in [0, 2], then

If a differentiable function f (x) has a relative minimum at x = 0, then the function y = f i.e. y = f (x) + ax + b has a relative minimum at x = 0 for

For f (x) = (x - 1)^2/3, the mean value theorem is applicable in the interval

Two towns A and B are 60 Km apart.A school is to be built to serve 150 students in town A and 50 students in town B.If the total distance to be travelled by all 200 students is to be as small as possible, then the school should be built at

The least value of a such that the function x²+ax+1  is increasing on (1,2) is

Minimum value of f (x) = sin x in - π/2 ≤ x ≤ π/2 is

If x be real the minimum value of x² - 8x + 17 is

The two positive numbers whose sum is 16 and the sum of whose cubes is minimum

f (x) = 1 + [cos x] x, in 0 < x ≤ π/2