Fun facts about derivatives.

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Presentation transcript:

Fun facts about derivatives

Daffy-nition

Daffy-nition is a mathematical operation on the function f(x). The operator is the symbol

Derivative of a constant f (x) = constant, f ' (x) = 0

Constant multiplier f'(ax) = a f'(x)

Power rule

Meaning of the derivative slope of tangent line

When the derivative is positive, the function is increasing

When the derivative is negative, the function is decreasing

the function has a horizontal tangent When the derivative is 0 the function has a horizontal tangent

the function may have a max or a min, but... When the derivative is 0 the function may have a max or a min, but...

When the derivative is undefined the function might also have a min or a max

Values of x where the derivative is either 0 or does not exist are called CRITICAL POINTS of the function

You must remember to check the function at ALL critical points to find the function's mins and maxes

The product rule (fg) ' = f 'g + g'f

The quotient rule “lo dhi – hi dlo over lo lo”

is the derivative of the derivative The second derivative is the derivative of the derivative

The second derivative

The End …for now…