Applications Of Derivatives

The set of all values of '$a$' for which $f(x)=(a+2)x^3-3a{x}^2+9ax-1$ decreases for all real ...

For $f(x)=2x^3-9a{x}^2+12a^{2}x+1$, where $a>0$. Let $p$ and $q$ be the points of local maximu...

The acute angle between the curves $y=|x^2-1|$ and $y=1$ at their points of intersection in th...

Evaluate \lim_{x \to 0} \frac{x - \sin x}{x - \tan x}, a ratio of two third-order vanishing trigonom...

Define f(x) = x^2 for x \le 1 and f(x) = ax + b for x > 1; find a, b making f differentiable everywh...

A function defined as f(x) = \frac{1 - \cos 4x}{x^2} for x \neq 0 and f(0) = m is continuous; find m...

Using L'Hopital's rule or expansion, the limit \lim_{x \to 0} \frac{e^x - 1 - x}{x^2} evaluates to w...

Assertion: every differentiable function is continuous. Reason: differentiability requires the diffe...

Let p(x) = x^2 \sin(1/x) for x \neq 0 and p(0) = 0; which statement about p at the origin is correct...

For the greatest integer function, at how many points in the open interval (0,3) is g(x) = [x] + [-x...

Let q(x) = \max{x, x^3} for real x; determine the set of points where q is not differentiable.

If y = x^x for x > 0, then the derivative dy/dx evaluated through logarithmic differentiation equals...