Editing Derivative test (section)

===Example===
Say we want to perform the general derivative test on the function <math>f(x) = x^6 + 5</math> at the point <math>x = 0</math>. To do this, we calculate the derivatives of the function and then evaluate them at the point of interest until the result is nonzero.

: <math>f'(x) = 6x^5</math>, <math>f'(0) = 0;</math>

: <math>f''(x) = 30x^4</math>, <math>f''(0) = 0;</math>

: <math>f^{(3)}(x) = 120x^3</math>, <math>f^{(3)}(0) = 0;</math>

: <math>f^{(4)}(x) = 360x^2</math>, <math>f^{(4)}(0) = 0;</math>

: <math>f^{(5)}(x) = 720x</math>, <math>f^{(5)}(0) = 0;</math>

: <math>f^{(6)}(x) = 720</math>, <math>f^{(6)}(0) = 720.</math>

As shown above, at the point <math>x = 0</math>, the function <math>x^6 + 5</math> has all of its derivatives at 0 equal to 0, except for the 6th derivative, which is positive. Thus ''n''&nbsp;=&nbsp;5, and by the test, there is a local minimum at 0.