# Questions tagged [derivatives]

Questions on the evaluation of derivatives or problems involving derivatives (for example, use of the mean value theorem).

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### Hey guys can you give me a real life problem with solution that involves derivatives [closed]

So we had a project given by our teacher to make a presentation that shows real life problems that involves derivatives. Can you help me to have a real life problems with it's solution?
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### Under which conditions an uniform continuous function is Lipschitz?

I wonder under which conditions an uniform continuous function is Lipschitz. I know that if this function is defferentiable and has bounded derivates, then it is Lipschitz, but I am would like to get ...
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### Find the absolute maximum and minimum of $f(x) = \frac{1}{x} - \frac{2}{x^2}$ on $[-2,1]$

Note: Turns out this is a pretty tricky problem where we need to use techniques not developed in the chapter. We will go over this problem in class on Tuesday. Find the absolute maximum and minimum ...
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### Formula of a polynomial with n roots

I have been trying to solve this proof: My observations were: The polynomial could be rewritten in factored form: (x-c1)(x-c2)....(x-cn) The RHS could be rewritten as the sum of each c-term Taking ...
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### Find absolute extrema of $f(x)=\frac{14}{x+2}$ on $[0,\infty)$

Find absolute extrema of $f(x)=\frac{14}{x+2}$ on $[0,\infty)$ $Solution:$ The question is asking to find the absolute extrema of $f(x)$ on $[0,\infty)$, which means to find the points on the graph ...
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### Find the value of $r$ which minimizes the surface area of the can.

A cylindrical can with height $h$ metres and radius $r$ metres has a capacity of $2$ litres. (i) Find an expression for $h$ in terms of $r$. (ii) Hence find an expression for the surface ...
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### Derivative of a differentiable function.

Let $f$ is a differentiable function over $[a,b]$ and $f'(a)<0$, $f'(b)>0$. Prove that exist $x_0\in[a,b]$ such that $f'(x_0)=0$. I can see $f$ is a differentiable so it is continuous too, but ...
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