Applications of...

Let f be a real valued function defined on (0, 1) ∪(2, 4) such that f ‘(x) = 0 for every x, then

Let f (x) = x⁴  –4x, then

The slope of the tangent to the curve x = a sin t, y = a   at the point ‘t ’is

The minimum value of (x) = sin x cos x is  

In case of strict decreasing functions, slope of tangent and hence derivative is

Let f (x) = x³ −6x² +9x+18, then f (x) is strict decreasing in

Tangents to the curve  y = x³  at the points (1, 1) and (–1, –1) are

Let  f(x) = x²⁵ (1 −x)⁷⁵  for all  x ∈[0,1], then f (x) assumes its maximum value at

The stone projected vertically upwards moves under the action of gravity alone and its motion is described by x = 49 t –4.9  t²  . It is at a maximum height when

The function f (x) = 2 –3 x is

Let g (x) be continuous in a neighbourhood of ‘a ’and g (a) ≠0. Let f be a function such that f ‘(x) = g(x) (x −a)² , then

Minimum value of the function f(x) = x² +x+1 is

If the line  y=x  is a tangent to the parabola  y=ax2+bx+c  at the point  (1,1) and the curve passes through  (−1,0), then

The function  f  (x) = | x  | has

At which point the line x/a + y/b = 1, touches the curve  y = be-x/a