If C is any constant andf(t)=Ct, then what isf(t)?

The height of a missile at time t is given byf(t)=at^2+bt, where a and b are constants. Find the function which gives the rate of change of the missiles height.

Find the equation of the tangent line tof(x)=x^3+x^2+x+1at x=4.

y=

Supposef(x)=3x^2+4

(a) What isf(x)

Now findf(x) by differentiating your formula forfabove. (f(x) is called the second derivative off(x)).

A sphere of radius r has volumeV(r)=4/3r^3. Find the rate of change of volume with respect to radius.

What quantity for the sphere does the formula forV(r) give.

A piece of PVC pipe which is open at both ends encloses a volumeV(r,l)=r^2l, where r is the radius of the pipe and l is its length. Suppose for a fixed length l we vary the radius r of the pipe. What is the rate of change of volume with respect to radius?

What quantity does the formula for this rate give?

A square with side length x has areaA(x)=x^2. Find the rate of change of area with respect to side length

Find the equation of the tangent line toy=x^2+x at x=1.

y=

Find the equation of the tangent line with slope 5 toy=2x^23x.

y=

A tin can with a circular base has a volume of64cm^3 and the surface area of the vertical (curved) side is32cm^2. What are the dimensions of the can?

Radius =

Haight=