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Tangent Line Approximation

The red line is the tangent line to the blue curve f(x) at the point A. We are comparing the function value with a tangent line approximation. Drag the slider to adjust the value of b, which is the x-coordinate of the point we are approximating. Questions: 1) What makes the tangent line approximation more or less accurate? 2) Why is the tangent line approximation always too small?