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(Solved by Expert Tutors) If C is any constant and?f(t)=Ct, then what is?f?(t)??Th

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)=4/3?r^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)=?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 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?64?cm^3 and the surface area of the vertical (curved) side is?32?cm^2. What are the dimensions of the can?

Radius =

Haight=

?

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