Let's find the quadratic polynomial q(x) = ax+bx+c where a, b, c are parameters to be...

 

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Let's find the quadratic polynomial q(x) = ax²+bx+c where a, b, c are parameters to be determined so that q(a) best approximates the graph of f(x) = ln(x) at x = 1. (a) We want to choose a, b, c such that our quadratic polynomial resembles f(x) at x = 1. First thing, we want f(1) = g(1). What equation in a, b, c does this condition give you? A. a+b+c=1 C. c = 0 B. a+b+c=0 D. c = 1 (b) We also want f'(1) = q'(1). What equation in a, b, c does this condition give you? (c) Finally, we want f"(1) = q"(1). What equation in a, b, c does this condition give you? (d) Find a solution to this system of linear equations! Your answer will give you values of a, b, c that can be used to draw a quadratic approximating the natural logarithm. You can check your answer on Desmos https://www.desmos.com/calculator/bad2xrwmv] Let's find the quadratic polynomial q(x) = ax²+bx+c where a, b, c are parameters to be determined so that q(a) best approximates the graph of f(x) = ln(x) at x = 1. (a) We want to choose a, b, c such that our quadratic polynomial resembles f(x) at x = 1. First thing, we want f(1) = g(1). What equation in a, b, c does this condition give you? A. a+b+c=1 C. c = 0 B. a+b+c=0 D. c = 1 (b) We also want f'(1) = q'(1). What equation in a, b, c does this condition give you? (c) Finally, we want f"(1) = q"(1). What equation in a, b, c does this condition give you? (d) Find a solution to this system of linear equations! Your answer will give you values of a, b, c that can be used to draw a quadratic approximating the natural logarithm. You can check your answer on Desmos https://www.desmos.com/calculator/bad2xrwmv]