Telangana Board Solutions for Chapter: Applications of Derivatives, Exercise 5: Exercise 10(e)

The distance-time formula for the motion of a particle along, a straight line is $s=t^3-9t^2+24t-18$. Find when and where the velocity is zero. 

Assume that an object is launched upward at $980 \frac{\mathrm{m}}{\sec }$, Its position would be given by $s=-4.9t^2+980t$. Find the maximum height attained by the object.(Answer without units)

Let a kind of bacteria grow in such a way that at time $t \sec$, there are $t^{(3/2)}$ bacteria. Find the rate of growth at time $t=4$ hours.   [correct up to three decimal places]

Suppose we have a rectangular aquarium with dimensions of length $8 \mathrm{m}$, width $4 \mathrm{m}$ and height $3 \mathrm{m}$. Suppose we are filling the tank with water at the rate of $0.4 \frac{{\mathrm{m}}^3}{\sec }$. How fast is the height of water changing when the water level is $2.5 \mathrm{m}$.(Answer without units)

A container is in the shape of an inverted cone has height $8 \mathrm{m}$and radius $6 \mathrm{m}$ at the top.It is filled with water, at the rate of $2 \frac{{\mathrm{m}}^3}{\mathrm{minute}}$. If the height of water changes by $\frac{k}{\mathrm{\pi }}$ when the level is $4 \mathrm{m}$, then find the value of $k$

The total cost $C\left(x\right)$ in rupees associated with the production of $x$ units of an item is given by $C\left(x\right)=0.007x^3-0.003x^2+15x+4000$ Find the marginal cost when $17$ units are produced.

The total revenue in rupees received from the sale of $x$ units of a product is given by $R\left(x\right)=13x^2+26x+15$. Find the marginal revenue when $x=7$.

A point $P$ is moving on the curve $y=2x^2$. The $x$-coordinate of $P$ is increasing at the rate of $4$ units per second. Find the rate at which the y coordinate is increasing when the point is at $(2,8)$.     [Enter the answer excluding units]