Applicartions Of Derivatives Test

Let f (x) = \({({x^2} - 4)^{1/3}}\), then f has a

The function f (x) = \({x^3}\) has a

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

The stone projected vertically upwards moves under the action of gravity alone and its motion is described by x = 49 t – 4.9 \({t^2}\) . It is at a maximum height when

The function \(f{\text{ }}\left( x \right){\text{ }} = {\text{ }}\left| {{\text{ }}x{\text{ }}} \right|\) has

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

Let f (x) be differentiable in (0, 4) and f (2) = f (3) and S = {c : 2 < c < 3, f’ (c) = 0 } then

Every continuous function is

Rolle’s Theorem is not applicable to the function \(f\left( x \right){\text{ }} = {\text{ }}\left| {{\text{ }}x{\text{ }}} \right|\) for \( - 2 \leqslant x \leqslant 2\) because

If \(x \in \left( {0,\frac{\pi }{2}} \right),\) then

Rolle’s theorem is not applicable to function f(x) = | x | in the interval [ – 3, 3] because

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

Let f (x) satisfy the requirements of Lagrange’s mean value theorem in [0, 2] . If f (0) = 0 and f ‘ \((x) \leqslant \frac{1}{2}\) for all in [0, 2], then

\(\mathop {\lim }\limits_{x \to \infty } f(x)\), where f (x) = \(\sqrt {\frac{{x - \sin x}}{{x + {{\cos }^2}x}}} \), is equal to

For a real number x, let [x] denote the greatest integer less than or equal to x thenf (x) = \(\frac{{\tan (\pi [x - \pi ])}}{{1 + {{[x]}^2}}}\)is