If C is any constant and f(t)=Ct, then what is f′(t)? 

The height of a missile at time t is given by f(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 to f(x)=x^3+x^2+x+1 at x=4.

y=

Suppose f(x)=3x^2+4

(a) What is f′(x)

Now find f′′(x) by differentiating your formula for f′above. ( f′′(x) is called the second derivative of f(x)).

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

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

A piece of PVC pipe which is open at both ends encloses a volume V(r,l)=πr^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 area A(x)=x^2. Find the rate of change of area with respect to side length

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

y=

Find the equation of the tangent line with slope 5 to y=2x^2-3x. 

y=

A tin can with a circular base has a volume of 64πcm^3 and the surface area of the vertical (curved) side is 32πcm^2. What are the dimensions of the can?

Radius =

Haight=