Explain why f(x + h) - f(x - h)/2h should give a reasonable approximation of f (

Question

Explain why f(x + h) - f(x - h)/2h should give a reasonable approximation of f (x) when h is small. Choose the correct answer below. A. The formula f(x + h) - f(x)/h gives the slope of the secant line that goes from -x to x + h. Its limit as h goes to 0 is f'(x). The formula f(x + h) - f(x - h)/2h gives the slope of the secant line that goes from h -x to x + h. Its limit as h goes to 0 is also f'(x). So for a small h. this would be a reasonable approximation of f'(x). B. The formula f(x + h) - f(x)/h gives the slope of the secant line that goes from x to x+ h. Its limit as h goes to 0 is f'(x). The formula f(x + h) - f(x - h)/2h gives the slope of the secant line that goes from x - h to x + h. Its limit as h goes to 0 is also f'(x). So for a small h. this would be a reasonable approximation of f'(x). C. The formula f(x + h) - f(x)/h gives the slope of the tangent line that goes from x to x + h Its limit as h goes to 0 is f'(x). The formula f(x + h) - f(x - h)/2h gives the

Explanation / Answer

Option B is correct one.

The average rate of change gives the slope of secant line from x to x+h.its limit approach f'(x) as h tends to 0.f'(x) gives the slope of tangent.

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