(Calculus)Tests

Vertical Line Test tests if a function is actually a function. How’re you gonna have 2 outputs for the same input.

Horizontal Line Test tests if a function is invertible.

First Derivative Test:

Tests if something is a critical point. (Or just gets you the slope - whatever way of thinking you prefer.)

Conditions

If $FDT=0$ or $FDT=\varnothing$, then it’s a critical point.

Second Derivative Test:

Tests if a critical point a local max or minimum.

Conditions

If:

• $f^{\prime \prime }(c)<0$, local max
• $f^{\prime \prime }(c)>0$, local min
• $f^{\prime \prime }(c)=0$, inconclusive

A related concept is the Point of Inflection!