Derivatives: 2.1-2.6 Quiz

Formulas to Know!!!

Average Rate of Change: f(b) - f(a) / b-a

Instantaneous Rate of Change: limit as h→ [f(x+h) - f(x)] / h

Another Instantaneous ROC (with value): f(x) - f(a) / x-a as lim x→a

Tangent line equation: (y-y1) = m(x-x1)

• M means slope!!

Derivative Formulas

Derivative Notation (many options!)

• f’(x)

• f’(number)

• dy/dx

• d/dx

• y’

Is it Differentiable, Continuous, Neither, or Both?

Continuous

When the limit of the function from both sides are equal, and the value of the function at the value being approached is equal to the limits, it is continuous!!

The value is important due to the fact of point discontinuities that are possible.

Differentiable

If the limits of the derivatives are equal to each other, and the value of the function at that value is equal, too, then it is differentiable. Must use the derivative of it!!!

A function can be one or the other, or neither, or both! It’s all possible.

Practice here!