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In many textbooks the derivative (or IROC) is described in terms of and (delta ) instead of and

  1. Explain why and are equivalent.

     can be translated as 'change in .' typically appears in the expression: . How are these equivalent?

  2. Use the diagram at right and the definition of IROC to write the slope of the tangent line in terms of and .

    'Definition of the Derivative' is the same thing as 'Instantaneous Rate of Change': IROC

Downward parabola, with x axis enclosing the parabola on the bottom side, with 2 dashed vertical lines between curve & x axis, labeled, x, &, x + delta x, with 2 increasing lines, one labeled, slope = f prime of x, tangent to the curve at dashed line, x, & other passing through the 2 points at the top of the 2 dashed lines.