Question

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"?

Answer 1

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:\[|f'(0.75)-\frac{f(0.75+\Delta x)-f(0.75)}{\Delta x}|\le0.1\]

Answer 2

The calculation is done for you by the mathlet though.

Answer 3

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!