Derivative at a point
Instructions: 1. Enter any function you like in the text box. e.g. x^2, exp(x), ln(x), sin(x) 2. Uncheck 'enter function' after entering the function to check if your input has been successfully recognized. 3. Hold down 'shift' and drag to adjust the view if necessary. You can also adjust the scale by holding down 'shift' and drag the axis. 4. Specify the red point. 5. Drag the pink point to anywhere you like, but make sure it does not overlap with the red point. 6. Depending on your needs, select the relevant 'show' boxes to aid your understanding. (Recommended: click the boxes from left to right, top to bottom.) 7. Drag the pink point towards the red point (alternatively, you can use the arrow keys on your keyboard). Observe how the slope of the cyan line changes when it gets closer and closer to the red point. 8. Eventually, when the pink point overlaps with the red point, the cyan line will become a tangent, shown in green. The slope of this tangent is also known as the derivative of the function at a point (the red point you have specified). 9. Repeat steps 1 to 8 if necessary.
Tasks: Find the derivative of the following functions at different points: 1. x^2 2. Any polynomial function you like (e.g. -2x^5+3x^4+1/2x^2-6x+5) 3. exp(x) 4. ln(x) 5. log(x) 6. sin(x) 7. cos(x) 8. tan(x) For interested students: 9. Any logistic function (e.g. 1/(1-e^(-x)) ) 10. Any rational function (e.g. (x+1)/(x-1) ) 11. abs(x) , especially at x = 0 12. sgn(x) , especially at x = 0 Created for SCNC1111 Calculus Tutorials Applicable topics: L5. First principles