The distance covered by a particle in $t$ seconds is given by $x = 3 + 8t - 4t^2$. After $1$ second,the velocity will be:

$A$ point is moving on $y=4-2x^2$. The $x$-coordinate of the point is decreasing at the rate of $5 \text{ units/s}$. Then,the rate at which the $y$-coordinate of the point is changing when the point is at $(1, 2)$ is

If the radius $r$ of a sphere is increasing at a rate of $2 \text{ cm/s}$,then the rate of change of its surface area is proportional to which of the following?

$A$ rod $AB$,$13 \text{ feet}$ long,moves with its ends $A$ and $B$ on two perpendicular lines $OX$ and $OY$ respectively. When $A$ is $5 \text{ feet}$ from $O$,it is moving away at the rate of $3 \text{ feet/sec}$. At this instant,$B$ is moving at the rate of:

If $r$ is the radius of a spherical balloon at time $t$ and the surface area of the balloon changes at a constant rate $K,$ then ....

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