Derivatives+&+The+Graph+of+the+Function

media type="custom" key="5944949" flat toc =Applications of Derivatives (Derivatives & The Graph of the Function)= It is expected that students will use the first and second derivatives to describe the characteristic of the graph of a function.

It is expected that students will:
 * given the graph of [[image:http://www.bced.gov.bc.ca/irp/math1012/images/calc259.GIF width="44" height="15" align="baseline"]]:
 * [[image:http://www.bced.gov.bc.ca/irp/math1012/images/calc260.GIF width="175" height="17"]]
 * relate the sign of the derivative on an interval to whether the function is increasing or decreasing over that interval.
 * relate the sign of the second derivative to the concavity of a function.
 * determine the critical numbers and inflection points of a function.
 * Determine the maximum and minimum values of a function and use the first and/or second derivative test(s) to justify their solutions
 * use Newton’s iterative formula (with technology) to find the solution of given equations, [[image:http://www.bced.gov.bc.ca/irp/math1012/images/calc261.GIF width="44" height="15"]]
 * use the tangent line approximation to estimate values of a function near a point and analyze the approximation using the second derivative.