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I cannot understand solution of Problem 3(C) in Secants and Tangents Problem set for session 1 introduction of derivatives. Can anybody post explanation for that.

OCW Scholar - Single Variable Calculus
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Notice how the app shows you values for dy/dx and also Δy/Δx? It's asking you to set x to 0.75 and play with the Δx slider to find all the Δx's that bring Δy/Δx and dy/dx within 0.1 units of each other. When x = 0.75 the app shows us that dy/dx is -0.16. So basically it is asking you to find all Δx's where Δy/Δx is between -0.06 and -0.26. I've included an attached image where Δy/Δx is -0.06 (that is 0.1 exactly units away from dy/dx so that is within the 0.1 range). There are many more places where Δy/Δx is within 0.1 units. Think you can find the rest of them now? : )

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