Today, again, like all the other days, we had to do problems on the board. These problems were like reviews of last friday's class on how to differentiate functions implicitly. Again we differentiate functions implicitly when the function is not in the y=f(x). We are reminded not to make little mistake like negative signs and forgetting to use the chain rule when differentiating y.
We had two questions on the board. First was about differentiating and finding the equation of the of the tangent line and next was about the related rates of change. For the related rates of change we apply everything we learned from before. For these kind of questions, we are not given a formula to use. We need to analyze the question to find out what we need to do. For example
***** All edges of a cube are expanding at a rate of 3 cm/min. how fast is the surface area changing when each edge is
a) 1 cm.
Surface Area = 6x^2 <----------------- this formula of surface area is static ( no changes) to make it dynamic, we have to take the derivative of this formula with respect to time. d S.A./dt = 12x(dx/dt) next we found out that 3 cm/min is the rate of how much the sides are changing. thus it equals to (dx/dt) therefore we just substitute what is given to our derived formula x=1 (dx/dt) = 3 to find the rate of change of the surface area.
d S.A./dt = 12(1)(3) = 36 <--------------- at that instant the rate of change of the surface area is 36
To conclude, there are a lot of other problems like this which uses other formulas. The key is analyze what is being given to you and understand what you need to do.
Thats it... the next scribe is xun :D