9.6

reflective- constrained optimization is key in determining the maximum efficiency of a function.

difficult- out of all the material we have covered thus far this has been the most difficult. there is a lot of material to grasp at once, but once i start doing more problems, ill become much more confident with the material.

4.3

reflective- the idea of global maxima/minima further expands on local max/min. This means that where as local max/min occur at nearby points, global maxima/minima occur at all other points.

difficult- when calculating global maxima/minima, one must remember to calculate all specific critical points within the interval.

4.2

reflective- finding the point of inflection is very similar to finding max/min. you make the 2nd derivative =0.

difficult- I have covered point of inflections thoroughly in my previous calc class.

4.1

reflective- by finding the local maxima/minima, one can better assess the derivative in graphical form.

difficult- one must remember that to find max/min, one must make the derivative = 0.

2.4

reflective-2nd derivatives allow one to further expand functions to other numbered derivatives, for example, 3rd derivatives, etc.

difficult- i have already done 2nd derivatives so they are no difficult to do. They are the same to calculate as first derivatives.

9.4

reflective- Finding partial functions algebraically gives me the sense that I have more control over the problem because of the computation necessary to complete the problem. In such problems, you plug in numbers rather than estimating.

difficult- The derivative problems in this section are similar to the ones in 9.3 so it's not that hard.

9.3

reflective- I enjoy finding the derivative of a function, but find estimating derivatives somewhat annoying, especially know that we have to watch if the deriv. of f is with respect to either x and y.

difficult- this isn't really difficult, just kind of annoying to do. One just has to watch out for what f corresponds to.

3.5

reflective- finding the derivatives of sinx and cosx are crucial, but only the start of other differentiable trig functions, such as tanx, secx, cscx, and cotx.

difficult- I am very confident with derivatives. In fact, I actually enjoy differentiating problems, so I look forward to differentiating future functions.

3.4

reflective- the product and quotient rule is very important to use, since future functions will be much more complex than they are now and may require several differential rules such as product and quotient.

difficut- these rules are easy to understand, but one must remember that the numerator gets differentiated first, then the denominator, and that the denominator is squared.

3.3

reflective- The chain rule is a necessary mathematical application because there are many functions which require several operations to differentiate it. for example, in (3(t^3)-t)^5 you have to differentiate the whole function as well as what is inside.

difficult- Chain rules are pretty easy, but they can get somewhat complex. One thing to keep in mind is to no forgot to differentiate the inside of the function.

3.2

reflective- it is interesting to see the relationship of graphs between the graph of an exponential funct. and the graph of the deriv. of that same exponential funct.

difficult- One may forget that the derivative of lnx is 1/x and the deriv. of e^x is e^x.

3.1

reflective- Finding the derivative of a function allows one to insert values and get actual values rather then having to estimate one.

difficult- this is relatively easy because i have done it before, but one can easily forget to subtract 1 from the exponent, especially if the exponent is negative.