Effect of Translations on the Derivative
As we translate a function, what happens to its derivative?
Use the sliders to investigate this below. A quadratic function and its derivative are visible by default. Move slider p to translate the function horizontally and q to translate it vertically, then move both sliders at the same time. What do you notice?
Use the circles next to the function definitions to make the quadratic functions invisible, then reveal the exponential function and its derivative. Repeat your investigation.
Do this one more time for the sinusoidal function and its derivative.
What can you conclude?
Which of the following best describes how translations affect the derivative?