Maxima and Minima Questions

Let f(x) = x2 + 1x2 and g(x) = x - 1x x∈R - {-1, 0, 1}. If h(x) = f(x)g(x) then the local minimum value of h(x) is :...

For x ∈ , define f(x). Then f has

Let f: R → R be defined by f(x) = . If f has a local minimum at x = - 1, then a possible value of k is

If , then the maximum value of Z is equal to

Suppose the cube x3 - px + q has three distinct real roots where p > 0 and q > 0. Then which one of the following holds?

If p and q are positive real numbers such that p2 + q2 = 1, then the maximum value of (p + q) is

If |z + 4| ≤ 3, then the maximum value of |z + 1| is

If x is real, the maximum value of is

If then the difference between the maximum and minimum values of u2 is given by

With two forces acting at a point, the maximum effect is obtained when their resultant is 4N. If they act at right angles, then their resultant is 3N. Then the forces are

The real number x when added to its inverse gives the minimum value of the sum at x equal to

If the function f(x) = 2x3 - 9ax2 + 12a2 x + 1, where a > 0, attains its maximum and minimum at p and q respectively such that p2 = q, then a equals...

The total number of local maxima and local minima of the function f (x) =

f : → R, If f(x) = loge ((sin x)sinx + 1), then the minimum value of f(x) is :

On the interval [0, 1] the function x25 (1 - x)75 takes its maximum value at the point -

The value of ′a′ so that the sum of the squares of the roots of the equation x2 -(a - 2 )x - a + 1 = 0 assume the least value is -

The slope of the tangent to the curve y = -x3 + 3x2 + 9x - 27 is maximum when x equals -

The positive real number x when added to it′s reciprocal gives the minimum value of the sum at x equal to -

If the function f(x) = 2x3 - 9ax2 +12a2x +1 where a > 0, attains it′s maximum and minimum at p and q respectively such that p2 = q then ′a′ equals -...

If f(x) = 1 + 2x2 + 4x4 + 6x6 + ..... + 100x100 is a polynomial in a real variable x, then f(x) has -