Find the best linear approximation to the function p(x) = -x³ + 3x at the point (2, -2). A) L(x) = 16 - 9x B) L(x) = 9x - 20 C) L(x) = 14 - 8x D) L(x) = 8x - 18 E) L(x) = 20 - 9x

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Quizplus · Accepted Answer

The linear approximation to a function f(x) at a point (a, f(a)) is given by L(x) = f(a) + f'(a)(x - a).For the given function p(x) = -x^3 + 3x, we have p(2) = -2 and p'(x) = -3x^2 + 3. So, p'(2) = -9.Therefore, the linear approximation to p(x) at the point (2, -2) is L(x) = -2 - 9(x - 2) = 16 - 9x.

Find the Best Linear Approximation to the Function P(x) =