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"?

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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"?

MIT 18.01 Single Variable Calculus (OCW)
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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:\[|f'(0.75)-\frac{f(0.75+\Delta x)-f(0.75)}{\Delta x}|\le0.1\]
The calculation is done for you by the mathlet though.
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!

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