Quick question about calculus (derivatives)

In summary, understanding differentiation is crucial in solving problems involving a graph. However, in cases where a graph is not provided, it is still possible to find the maximum/minimum value by applying the formula and using differentiation rules. It is helpful to have both a graph and formula for a better understanding and accuracy in finding solutions. In the given examples, the area function serves as the graph. It is important to have a clear understanding of differentiation to avoid any misconceptions.
  • #1
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
 
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  • #2
a129 said:
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##.
 
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  • #3
a129 said:
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.
a129 said:
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.
a129 said:
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
 

Related to Quick question about calculus (derivatives)

1. What is a derivative in calculus?

A derivative in calculus is a measure of how a function changes when its input changes. It is defined as the slope of a tangent line to a curve at a specific point.

2. Why are derivatives important in calculus?

Derivatives are important in calculus because they allow us to understand and analyze the behavior of functions. They help us find maximum and minimum values, determine the rate of change of a function, and solve optimization problems.

3. How do you find the derivative of a function?

To find the derivative of a function, you can use the power rule, product rule, quotient rule, or chain rule. These rules involve taking the limit of a difference quotient, which can be simplified using algebra and trigonometry.

4. What is the difference between a derivative and an antiderivative?

A derivative measures the rate of change of a function, while an antiderivative is the reverse process of differentiation. In other words, an antiderivative is a function that, when differentiated, gives the original function.

5. How are derivatives used in real life?

Derivatives are used in various fields, such as physics, engineering, economics, and finance. In physics, they are used to calculate velocity and acceleration. In economics, they are used to analyze demand and supply curves. In finance, they are used to calculate risk and optimize investment strategies.

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