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<h2>The slope of the line tangent to the function at x = 1 is 2.01 ≅2.</h2>Step-by-step explanation:
Using the formula of derivative, it can be easily shown that, where
.
Here we need to show that as per the instructions in the given table.
Δy = f(x + Δx) - f(x) = f(1 + 0.01) - f(1) = .
In the above equation, we have put x = 1 because we need to find the slope of the line tangent at x = 1.
Hence, dividing Δy by Δx, we get, .
Let's examine this taking a smaller value.
If we take Δx = 0.001, then Δy = .
Thus, .
The more smaller value of Δx is taken, the slope of the tangent will be approach towards the value of 2.