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B Quick question about calculus (derivatives)

  1. Sep 1, 2017 #1
    I thought Differentiation is all about understanding it in a graph. Every time I solve a question on differentiation I visualise it as a graph so it's more logical. After all, that IS what the whole topic is about, right? Or am I just wrong?

    But when you look at these questions:

    It's asking for the maximum/minimum value, and my question here is where is the graph? How do I find the maximum/minimum value without a graph? I can't imagine the graph

    It's probably doable by just applying the formula, but seeing it in a graph would make sense.

    If a question would be something like a person filling a cylinder of height x with water of volume 2cm^3 per second, then sure I can imagine the graph and I can find the rate of change..

    So for these questions..how do the graphs look like? Or maybe there isn't any graph for it? I'm worried, I hope I didn't grasp on the wrong concept all this time..

    Thanks! I really need some answers

    EDIT: Im not asking for the answer. So I thought it's appropriate to post this on here instead of on the homework section
  2. jcsd
  3. Sep 1, 2017 #2


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    Staff: Mentor

    In this case, you need to have first a function ##f## which can be differentiated. The graph is then ##\{(x,f(x))\,\vert \,x \in D\}## with ##D## being the domain of allowed values for the variable ##x##.
    Last edited: Sep 1, 2017
  4. Sep 1, 2017 #3


    Staff: Mentor

    In the two problems you circled in the image you posted, the graph would be the area function. In the first problem, you have area as a function of r. In the second problem, area is a function of x.
    It's advantageous to have both a graph of the function and its formula. Seeing the graph would give you a rough idea where a maximum or minimum would be, but using differentiation rules would give you the exact value.
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