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## Related Questions

###### Asked in Calculus

### How do you find minimum and maximum value of calculus?

In Calculus, to find the maximum and minimum value, you first
take the derivative of the function then find the zeroes or the
roots of it. Once you have the roots, you can just simply plug in
the x value to the original function where y is the maximum or
minimum value. To know if its a maximum or minimum value, simply do
your number line to check. the x and y are now your max/min points/
coordinates.

###### Asked in Math and Arithmetic, Statistics, Algebra

### How do you determine wheather a quadratic function has a maximum or minimum and how do you find it?

In theory you can go down the differentiation route but because
it is a quadratic, there is a simpler solution.
The general form of a quadratic equation is y = ax2 + bx + c
If a > 0 then the quadratic has a minimum
If a < 0 then the quadratic has a maximum
[and if a = 0 it is not a quadratic!]
The maximum or minimum is attained when x = -b/2a and you
evaluate y = ax2 + bx + c at this value of x to find the maximum or
minimum value of the quadratic.

###### Asked in Math and Arithmetic, Algebra

### How do you know if a point is a maximum or a minimum?

Usually at the minimum or maximum of a function, one of the
following conditions arises:
The derivative is zero.
The derivative is undefined.
The point is at the end-points of the domain that is being
considered (or of the naturally-defined domain, for example, zero
for the square root).
This will give you "candidate points"; to find out whether each
of these candidate points actually is a maximum or a minimum,
additional analysis is required. For example, if the second
derivative is positive, you have a minimum, if the second
derivative is negative, you have a maximum - but if it is zero, it
may be a maximum, a minimum, or neither.

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