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. O A. f(x+h)-f(x) h f(x+h)-f(x-h) gives the 2h The formula 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 slope of the tangent 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). B. f(x+h)-f(x) h f(x+h)-f(x-h) 2h The formula 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 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 this would be a reasonable approximation of f'(x). f(x+h)-f(x) The formula 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 gives the h tangent 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). f(x+h)-f(x-h) 2h slope of the D. f(x +h)-f(x) The formula 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 gives the h 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 this would be a reasonable approximation of f'(x). f(x+h)-f(x-h) 2h
