Q1-3 are very standard questions. You are should not have problems.
Q4. A similar question was done in class. Check your class ntoebook.
Q5a. Find dy/dx. (you should know what rule to use)
Q5b. At stauionary points, dy/dx = ? (hence you can solve to find x)
Q6.
Just do your dy/dx first.
Then, ask yourself: What is the dy/dx at the stationary point?
Since the stationary point is at (3, 5), the value of x is 3.
Substitute into dy/dx and you get 1 linear eqn.
At this point, x=3 and y=5. Substitute into original equation and you should get another linear eqn.
Solve simultaneously.
Q7 to 10 are quite similar.
All of you should be able to do dy/dx and find the x-coordinates of the stationary points.
What does nature of the stationary points mean?
Whether they are minimum, maximum or point of inflexion. (check textbook examples)
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teacher i do some rate of change questions today, I found the main problem for me is sometime I do not know how to gain the information from the question.(做题时逻辑比较混乱)Do you have any good suggestion for me?
ReplyDeleteUnderline important phrases. e.g. rate of change of y, x is increasing at a rate of, the volume is increasing at a rate of....
ReplyDeleteThen you will see more clearly. In every question there must be a main formula. E.g. formula for volume of sphere or a function in terms of y.
All other information will be given by the question. You need to sieve them out.
If question is in y=5x^3+.... types, you look for (a) rate of increase of y and (b) rate of increase of x. if (a) is given, question will ask u to find (b). If (b) is given, question will ask you to find (a). For dy/dx, you will differentiate on your own. x will be given by question. However, sometimes question give you y, and you need to use this to find x on your own.
Thanks ^_^
ReplyDelete