Calculating Rates of Change in Calculus Problems

[Hollysmoke]

Our teacher gave us some extra challenge questions and I've solved them all except for two, which has been really bugging me:

1) Determine the equation of a line that passses through (2,2) and is parallel to the line tangent to y=-3x^3-2x at (-1,5)

2) estimate the instantaneous rate of change of the surface area of a sphere with respect to its radius when the radius is 10cm.

I don't want to know how to solve them but just a bit of help to get me along on my own would be nice. Thank you.

EDIT: I just realized I put this in the wrong thread. Is it possible to move it to the Intro Calculus thread? Thank you.

 

[dicerandom]

1) Two lines are parallel if they have the same slope. What's the slope of the tangent line to the curve at the point given?

2) What is the formula for the surface area of a sphere? How would you find how it changes with r?

 

[borisleprof]

Y may be know that the slope of the tangent is given by the value of the derivative at the pooint (-1, 5) . Knowing the slope, you will be able to determine the equation of the line.

2) You must know the rate of change of the radius.
Do you know how to calculate the surface area of a sphere in function of its radius?