Math  /  Calculus

QuestionHomework 6: Problem 4 (1 point)
Find the linearization L(x)L(x) of the function g(x)=xf(x2)g(x)=x f\left(x^{2}\right) at x=2x=2 given the following information. f(2)=0f(2)=6f(4)=3f(4)=4f(2)=0 \quad f^{\prime}(2)=6 \quad f(4)=3 \quad f^{\prime}(4)=-4
Answer: L(x)=L(x)= \square

Studdy Solution
Construct the linearization L(x) L(x) using the formula: L(x)=g(2)+g(2)(x2) L(x) = g(2) + g'(2)(x - 2) L(x)=629(x2) L(x) = 6 - 29(x - 2)
The linearization L(x) L(x) is:
629(x2) \boxed{6 - 29(x - 2)}

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