Program that uses integrals to calculate the maxima of a function.

#### Sample output:

``````
The function reaches a minimum at the input -3.160000000000039
The value of f(x) at this value is: -56.62509600000119 + constant
The function reaches a maximum at the input 0.009999999999937692
The value of f(x) at this value is: -31.626624990001016 + constant
The function reaches a minimum at the input 3.169999999999914
The value of f(x) at this value is: -56.6240009100012 + constant
```
```
``````import java.math.*;

public class calculateMaximaUsingIntegrals {

/**
* @param args
*/
public static void main(String[] args) {
// Write an equation using integrals that tests f(x) and determines the
// max and min points using the integral of the first derivative.
// This could be done by finding the first derivative, then take the sum
// of the product of the change of output and the change of input for
// all inputs. For each change of input,
// compare the previous product (that of the output and the input) to
// the following product, if there is a sign change (> or < zero), then
// a maximum or minimum value is found.
// If the sign change is from less than zero to greater than zero, there
// exists a minimum. If greater than zero to less than zero, there is a
// maximum. The sum corresponds
// to the value at the input.

//We're inputing the function f'(x). We're obtaining information about f(x).
double inputs[] = new double;
double outputs[] = new double;
double x = -5; // The starting x value
int i = 0;
double endx = Math.abs(x); // The ending x value
double h = .01; // The change in x values, decreasing this value
// increases accuracy
double outputold = 0;
double outputnew = 0;
double sum = 0;

while (x < endx) {
inputs[i] = x;
outputs[i] = (inputs[i]*inputs[i] * inputs[i])-(10*inputs[i]);
sum += (h*outputs[i]);
outputnew = outputs[i];
if (outputnew > 0 && outputold < 0) {
System.out
.println("The function reaches a minimum at the input "
+ x);
System.out
.println("The value of f(x) at this value is: " + sum +" + constant");

}
if (outputnew < 0 && outputold > 0) {
System.out
.println("The function reaches a maximum at the input "
+ x);
System.out
.println("The value of f(x) at this value is: " + sum +" + constant");

}
outputold = outputnew;
i++;
x += h;
}

}
}

```
```