Application of Derivative Questions

Let f(x) = x sin π x, x > 0. Then for all natural numbers n, f′(x) vanishes at -

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio of 8 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four co...

The real number k for which the equation 2x3 + 3x + k = 0 has two distinct real roots in [0, 1]

The intercepts on x-axis made by tangents to the curve, which are parallel to the line y = 2x, are equal to...

If p, q, r are any real numbers, then

If y = a log x + bx2 + x has its extremum values at x = -1 and x = 2, than

The normal to the curve x = a (cos θ + θ sin θ) y = a (sin θ - θ cos θ) any point ′θ′ is such that

Let p(x) = a0 + a1 x2 + a2x4 + ..... + anx2n be a polynomial ina real variable xwith 0 0 1 1 n The function P(x) has...

Let f and g be increasing and decresing functions respectively from [0, ∞) to [0, ∞) Let h(x) = f (g(x)). If h(0) = 0, then h(x) - h(1)

The function f(x) is

The slope of tangent to a curve y = f (x) in [x, f (x)] is 2x + 1 If the curve passes through the point (1, 2) then the area bounded by the curve, the x-axis and line x = 1 is...

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

If f(x) and g(x), where 0

The number of values of x, where the function f (x) = cos x + cos (√2x) attains its maximum, is

If f(x), for every nu8mber x, then the minimum value of f

The function f(x) = sin4 x + cos4 x increases, if

Let f(x) = ∫ ex(x - 1)(x - 2)dx. Then f decreases in the interval

Let f(x) = Then, at x = 0, f has

If the normal to the curve y = f (x) at the point (3, 4) makes an angle with the positive xaxis, then f′(3) is equal to...

If f(x) = xex(1-x), then f(x) is