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estimate the derivative

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The data in the table below define y as a function of x.
x 0 .5 1 1.5 2 2.5
y -1.4 1.025 4.6 9.325 15.2 22.225

A. Estimate the derivative at each of the following points using the average of the left and right difference quotients.
x1 0.5 1 1.5 2
slope 3.575/.5 4.725/.5 5.875/.5 7.025/.5

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This solution shows how to estimate the derivative at each of the following points using the average of the left and right difference quotients.

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for x1 = 0.5
the left difference quotient is: (f(0.5) - f(0.5-h))/h
where h = 0.5 from the given info;
so l = (f(0.5)-f(0))/0.5 = (1.025-(-1.4)/0.5 = 4.85

the right difference quotient is: (f(0.5 + h) - f(0.5)) /h
r ...

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