Exercise

The abscissa of a point moving along the curve $y^2=12x$ increases at the rate of $2 \mathrm{cm}/\sec .$ Then, the co-ordinates of the point, rates of increase of whose abscissa and ordinate are the same are

The largest value of the function $y=8-x^2$ is 

The function $f\left(x\right)=x^3-3x+3$ possesses a 

For a function $y=f\left(x\right), \frac{dy}{dx}=0$ at $x=a$, that mean

Find the values of $x$ for which $y=\left[x\right(x-2){]}^2$ is an increasing function.

Find the intervals in which the following function is strictly increasing or decreasing:
$6-9x-x^2$

Find the intervals in which the function $f$ given by $f\left(x\right)=2x^2-3x$ is strictly decreasing.

Find the intervals in which the following function is strictly increasing or decreasing:
$(x+1{)}^3(x-3{)}^3$