Question

How do I find the absolute maximum and minimum of a function?

Answer 1

In the given question, we have been asked how we can calculate the absolute maximum and the absolute minimum of a function. We calculate that by putting in the derivative to be equal to zero.

Formula Used:
The derivative of a function is calculated using:
$f'\left( {{x^n}} \right) = n{x^{n - 1}}$

Complete step by step answer:
In the given question, we are asked how we can calculate the absolute maximum and the absolute minimum of a function.
Consider we have a function, $f\left( x \right)$.
First, we find the derivative of $f\left( x \right)$.
The derivative is, $f'\left( x \right)$.
Now, we find the points where the derivative equals zero,
$f'\left( x \right) = 0$
Let the points be ${x_1},{x_2},...,{x_n}$.
Finally, we put in the points ${x_1},{x_2},...,{x_n}$ in the original function, $f\left( x \right)$ and find the value at each point, i.e., we find
$f\left( {{x_1}} \right),f\left( {{x_2}} \right),...,f\left( {{x_n}} \right)$
And we then pick up the value where $f\left( {{x_m}} \right)$ gives the maximum and minimum value for the function and the corresponding argument gives us the answer.

Note:
In the given question, we were how we can calculate the absolute maximum and the absolute minimum of a function. To do that, we first find the derivative of the function. Then we put the derivative equal to be zero. Then we find the point where it is equal to zero. And finally, we plug in the values in the original function and calculate from there. So, it is really important that we know the formulae and where, when, and how to use them so that we can get the correct result.