# Calculus - Minimum Value of a Function

Geometrically, the 1st derivative of a function is the slope of the curve.

When the 1st derivative is positive, the function is increasing.

When the 1st derivative is negative, the function is decreasing.

When the 1st derivative is zero, the function has reached a maximum, minimum, or an inflection point.

When the 1st derivative is zero. the 2nd derivative will show whether that point is a maximum, minimum, or an inflection point.

The 2nd derivative is the slope of the 1st derivative function.

The 2nd derivative is negative when the original function has reached a maximum (at that point where the 1st derivative is zero).

The 2nd derivative is positive when the original function has reached a minimum (at that point where the 1st derivative is zero).

The 2nd derivative is zero when the original function has reached a point of inflection (at that point where the 1st derivative is zero).

Determine the minimum value of the function y=3x^3+x^2-15x+2 for x<0.