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 Links

Functions, graphing, fancy, history (see 0  toc)

Derivatives Web Page

Reimann Sums gsp

ReimannSumNotes.pdf

Intro to Antiderivatives

Derivative Calculator at https://www.derivativecalculator.net/

Integral Calculator at https://www.integralcalculator.com/
 Activities
 * Use the above pages & calculators to assist in writing a test.
 1  LIMIT by approach
 Links

endbahavior.htm

limit.htm

limit.gsp

 Activities
 1st. Slide the x value to approach.
 * Take a limit, as x approaches c, where f(c) is continuous
 * Take a limit, as x approaches c, where f(c) is not continuous,
 as in x=c is a vertical asymptote
 * Take a limit, as x approaches infinity
 * Change the function & repeat the above
 * Examine endbehavior
 2  DERIVATIVE by definition, secant
 Links

limit.htm which includes
limit.gsp
 Show work

 Activities
 1st. Drag the red point to make h smaller, closer to 0, to make h approach 0, to obtain the derivative.
 2nd. As h gets smaller the secant line EF becomes more like a tangent line.
 3rd. Try to slide the red point so close to (x, f(x)) that the slope of the secant
equals the slope of the tangent, the derivative at (x, f(x)).
 3  DERIVATIVE by m of tangent line, x
 Links

TABLE f, f(x), f '(x), f " " (x) DerAnyFx.gsp then page 5
 also See No. 20 below reguarding "Derivative TABLE found in DerAnyFx.gsp"
 Show computation & functions

 Activities
 * Use Ctrl + C to make more emojis as needed.
 * Use emojis to mark status of the function.
 * Find & mark the zeros of the function.
 * Find & mark the zeros of the first derivative.
 * Discuss the status of the function at these points/values.
 * Find & mark the zeros of the second derivative.
 * Discuss the status of the function at these points/values.
 * Find & mark other values of C, f(C), f' (C), f ' ' (C).
 * Discuss intervals over which the function is increasing/decreasing/zero.
 * Discuss intervals over which the function is concave up/down.
 * Summarize as desired.
 * Change the function & repeat the questions/activities.
 4  DERIVATIVE by trace
 Links
 Hide/show trig memory trick
 Hide/show derivative functions
 Hide/show Teaching Activities.

 Hide/show 1st derivitive in green
 Hide/show 2nd derivitive in purple
 Hide/show 3rd derivitive in orange
 Hide/show 4th derivitive in red

 Activities
 Trace the derivatives.
 1st: Turn OFF then ON in Display Menu "Trace Point" OR use Ctrl + T.
 2nd: Drag the DOT ON THE AXIS to trace that color derivative.
 3rd: Erace the trace with Display Menu OR Shift + Ctrl + E.
 4th: Trace the derivatives.
 Teaching activities
 1. Enable the tracing, trace, name the dotdrawn derivative, record it on the screen w/pen
 2. Repeat step 1 with second derivative.
 3. Repeat step 1 with the next derivative.
 4. Repeat step 1 with the next derivative.
 5. Reflect on/Discuss the result of all graphs.
 6. Unhide the memory trick.
