Find the linearization of the function (f(x) = x^3 + 2x^2 - 3x + 1) at (x = 2).

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Accepted Answer

Step:1 ：The formula for the linearization (or the linear approximation) of a function (f(x)) at a point (a) is given by (L(x) = f(a) + f&#x27;(a)(x-a)).Step:2 ：First, we find (f(a)) by substituting (x = 2) into the function: (f(2) = 2^3 + 2(2^2) - 3(2) + 1 = 8 + 8 - 6 + 1 = 11).Step:3 ：Next, we find (f&#x27;(a)) by first finding the derivative of (f(x)), which is (f&#x27;(x) = 3x^2 + 4x - 3), and then substituting (x = 2) into the derivative: (f&#x27;(2) = 3(2^2) + 4(2) - 3 = 12 + 8 - 3 = 17).Step:4 ：Finally, we substitute (f(a)) and (f&#x27;(a)) into the formula for the linearization: (L(x) = 11 + 17(x - 2)).

Answer

Step: 1 ：The formula for the linearization (or the linear approximation) of a function (f(x)) at a point (a) is given by (L(x) = f(a) + f&#x27;(a)(x-a)).Step: 2 ：First, we find (f(a)) by substituting (x = 2) into the function: (f(2) = 2^3 + 2(2^2) - 3(2) + 1 = 8 + 8 - 6 + 1 = 11).Step: 3 ：Next, we find (f&#x27;(a)) by first finding the derivative of (f(x)), which is (f&#x27;(x) = 3x^2 + 4x - 3), and then substituting (x = 2) into the derivative: (f&#x27;(2) = 3(2^2) + 4(2) - 3 = 12 + 8 - 3 = 17).Step: 4 ：Finally, we substitute (f(a)) and (f&#x27;(a)) into the formula for the linearization: (L(x) = 11 + 17(x - 2)).

Find the linearization of the function $f (x) = x^{3} + 2 x^{2} - 3 x + 1$ at $x = 2$ .

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Popular Problems

Find the linearization of the function f(x)=x3+2x2−3x+1 at x=2.

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Popular Problems

Find the linearization of the function $f (x) = x^{3} + 2 x^{2} - 3 x + 1$ at $x = 2$ .