How can a linear approximation be used to approximate the value of a functionf near a point at which f and f' are easily evaluated? Choose the correct answer below. O A. Iffis differentiable at the point, then near that point, f is approximately linear; so, the function nearly coincides with the tangent line at that point. O B. Iffis differentiable at the point, then near that point, f is nonlinear; so, the function is equal to the tangent line at that point. OC. Iffis differentiable at the point, then near that point, f is approximately linear; so, the function is equal to the tangent line at that point. O D. Iff is differentiable at the point, then near that point, f is approximately linear; so every function value is less than the value of the tangent line at that point.

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A: Differentiate at given point and then use equation of  tangent  line

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: