Derivative practice

Work out the derivative of at the marked point and enter its value. The graph draws the line through with the slope you gave: a correct answer grazes the curve, a wrong one cuts across it.

Problem

Exact expressions welcome: pi/6, -2/e, sqrt(2)/2, 4/5.

Graph

×1

— magnified about the point, equally in both directions. The curve straightens as you go in: that is local linearity. A correct line settles onto it and disappears into it; a wrong one keeps its angle however far you zoom. Drag the graph to move it around; Reset brings it back.