Quick question about calculus (derivatives)

[a129]

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:
http://imgur.com/a/MdO6w

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: I am not asking for the answer. So I thought it's appropriate to post this on here instead of on the homework section

 

[fresh_42]

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

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 $x$.

 

[Mark44]

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:
http://imgur.com/a/MdO6w

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

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

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.

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: I am not asking for the answer. So I thought it's appropriate to post this on here instead of on the homework section