Find the equation of the tangent line to the curve y=-2x^2+\ln x-x at (1, -3).

Question:

Find the equation of the tangent line to the curve {eq}y=-2x^2+\ln x-x {/eq} at {eq}(1, -3) {/eq}.

Tangent Line:

The equation of the tangent line to a function f(x) at a point x0 is obtained linearizing

the function at that point, i.e. arresting the Taylor series of the function at the first order term

{eq}L(x) = f(x_0) + f'(x_0)(x-x_0) {/eq}

Answer and Explanation:

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The equation of the tangent line to the function

{eq}y(x)=-2x^2+\ln x-x {/eq}

at x = 1 is found linearizing the function at this point, i.e.

{eq}L...

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Linearization of Functions

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Chapter 10 / Lesson 1
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