Numerical Differentiation 1. Given the following data points: 0.3 0.4 0.5 0.6 0.7 y 1.3444 1.4728 1.5975 1.7053 1.7768 (a) Estimate f(0.48). (b) Estimate f'(0.48). (c) With the function given as f(x) = e* cos x², compare the values obtained in (a) and (b) by getting the actual values and the corresponding relative errors.

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A: Please check step 2 for the solution.!

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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: