Effect of Stretches on the Derivative

As we translate a function, what happens to its derivative?[br][br]Use the sliders to investigate this below. A quadratic function and its derivative are visible by default. Move slider [i]p[/i] to translate the function horizontally and [i]q[/i] to translate it vertically, then move both sliders at the same time. What do you notice?[br][br]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.[br][br]Do this one more time for the sinusoidal function and its derivative.[br][br]What can you conclude?

Which of the following best describes how stretches affect the derivative? (Check [i]all[/i] that apply.)

Vertical stretches result in vertical stretches only in the derivative No effect Horizontal stretches result in horizontal and vertical stretches in the derivative Vertical stretches result in horizontal and vertical stretches in the derivative Horizontal stretches result in horizontal stretches only in the derivative Horizontal stretches affect the derivative; vertical stretches do not Vertical stretches affect the derivative; horizontal stretches do not

Effect of Stretches on the Derivative

Information: Effect of Stretches on the Derivative