Derivatives

Graphing calculator

Pilgrim, are you up for a little mathematics? An important part of calculus is determining the slope of a curve at any point on that curve. This process is called taking the derivative … which is equivalent to the rate of directional change … better known as velocity.

Now calculus has a rather clever way of determining the equation for the derative of an equation … such as: y = 5x^3 - 9x^2 + 2x +14

Now, follow closely Pilgrim, to derive the first derivative, for each equation element, multiply the exponent times the coefficient and replace the old coefficient … then reduce the exponent by one. So, the derivative of the first element of the above equation is (3*5)x^2 … or 15x^2. Also note any x without an exponent becomes x^0 or just 1 … which means that just it’s coefficient survives. And any elements without an x (the y intercept) disappears because moving the same curve up or down the y-axis doesn’t change its slope anywhere.

If you have followed my short explanation, Pilgrim, you hopefully know that the first dirative of the full equation is: y = 15x - 18x + 2. Simple?

Then, to find the slope at any point in the original equation at any x value … say 3 … replace each x with 3 into the derivative equation to get  y = 15*3 - 18*3 + 2 … or -7. This means at the 3 point on the x axis the slope is downward 7 tiny units (delta) for  every tint unit (delta) to the right. If you have a graphing calculator, enter the original equation and check this result.

(Taking the derative of the derative equation is called the “second derative” and is a measure of acceleration/deceleration … often used in stock market analysis.)

You ask the $64 million question … why does this bit of black mathematical magic work? I have only the foggiest idea. But I’m sure Isaac Newton knew!

STAND UP FOR ISAAC NEWTON!