Application of Derivatives

A ladders $5 \mathrm{~m}$ long is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall, at the rate of $2 \mathrm{~m} / \mathrm{sec}$. The speed at which its height on the wall…

Quadrilateral PQRS is inscribed inside a rectangle of dimensions $10 \mathrm{~cm} \times 8 \mathrm{~cm}$. The value of ' $x$ ', if the area of the quadrilateral is minimum is

The dimensions of the largest rectangle of side $x$ and $y$ that can be inscribed in the right angled triangle of sides $\mathrm{a}$ and $\mathrm{b}$ is

$O A$ and $O B$ are two roads enclosing an angle of $120^{\circ} . X$ and $Y$ start from $O$ at the same time. $X$ travels along $O A$ with a speed of $4 \mathrm{~km} / \mathrm{h}$ and $Y$ travels along $O B$ with a…

The maximum area in square units of an isosceles triangle inscribed in an ellipses $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ with its vertex at one end of the major axis is

A circular sector of perimeter $60 \mathrm{~m}$ with maximum area is to be constructed, The radius of the circular arc in metre must be

$\underset{0\leq\,x\leq\,\pi\,}{\max\,}\left{x-2\sin\,x\cos\,x+\frac{1}{3}\sin\,3x\right}=$

Passage: Let $S$ and $T$ be the sets where $f(x)=\dfrac{x^3}{3}-\dfrac{5x^2}{2}+6x+7$ decreases and increases respectively. Question: What is $T$ equal to ?

Passage: Let $S$ and $T$ be the sets where $f(x)=\dfrac{x^3}{3}-\dfrac{5x^2}{2}+6x+7$ decreases and increases respectively. Question: What is $S$ equal to ?

Consider the following statements: The function $f(x)=\sin x$ decreases on the interval $(0, \pi / 2)$. The function $f(x)=\cos x$ increases on the interval $(0, \pi / 2)$. Which of the above statements is/are correct?

At an extreme point of a function $f(x)$, the tangent to the curve is

The radius of a circle is uniformly increasing at the rate of $3 \mathrm{~cm} / \mathrm{s}$. What is the rate of increase in area, when the radius is 10 cm ?