## anonymous 4 years ago I can't understand the meaning of Problem 1: (c) "Find a value of Δx for which the value of Δy/Δx is within 0.1 units of Δx the slope of the tangent line." What is the "0.1 units of the slope"?

1. TuringTest

The question is about how far off our secant estimate for the actual tangent is. Use the mathlet on the page and follow the instructions carefully. The size of delta x is what will determine how accurate our estimate is. The question basically asks for what value of delta x we have the estimation within 0.1 units (whatever the particular units are is not important here) of the actual value of the derivative at that point:$|f'(0.75)-\frac{f(0.75+\Delta x)-f(0.75)}{\Delta x}|\le0.1$

2. TuringTest

The calculation is done for you by the mathlet though.

3. anonymous

I seem to have been confused by the word "units". Aha, I should only take account of the difference between the slope of the tangent line and of the secant line. Thank you, TuringTest!