Concept+&+Interpretations

media type="custom" key="5944949" flat toc =The Derivative (Concept & Interpretations)= It is expected that students will understand the concept of a derivative and evaluate derivatives of a function using the definition of derivative.  It is expected that students will: >
 * describe geometrically a secant line and a tangent line for the graph of a function at x = a.
 * define and evaluate the derivative at x = a as: [[image:http://www.bced.gov.bc.ca/irp/math1012/images/calc240.GIF width="108" height="29" align="middle"]] and [[image:http://www.bced.gov.bc.ca/irp/math1012/images/calc241.GIF width="91" height="29" align="middle"]]
 * define and calculate the derivative of a function using:
 * use alternate notation interchangeably to express derivatives [[image:http://www.bced.gov.bc.ca/irp/math1012/images/calc243.GIF width="127" height="32" align="middle"]]
 * compute derivatives using the definition of derivative
 * distinguish between continuity and differentiability of a function at a point
 * determine when a function is non-differentiable, and explain why
 * determine the slope of a tangent line to a curve at a given point
 * determine the equation of the tangent line to a curve at a given point
 * for a displacement function [[image:http://www.bced.gov.bc.ca/irp/math1012/images/calc244.GIF width="37" height="15"]], calculate the average velocity over a given time interval and the instantaneous velocity at a given time
 * distinguish between average and instantaneous rate of change

Miscellaneous Resources
media type="file" key="The Derivative Song.mp3" width="240" height="20"

Touch Mathematics
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