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Find the equation of the tangent line to the curve of the function y=x^2 at the point P(2,4)

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Answer to a math question Find the equation of the tangent line to the curve of the function y=x^2 at the point P(2,4)

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Santino
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Para encontrar la ecuación de la recta tangente a la curva de la función y = x^2 en el punto P(2, 4), necesitamos determinar la pendiente de la recta tangente y usar la forma punto-pendiente de una ecuación lineal. . La pendiente de la recta tangente en un punto dado es igual a la derivada de la función evaluada en ese punto. Para la función y = x^2, la derivada viene dada por: dy/dx = 2x Para encontrar la pendiente de la recta tangente en el punto P(2, 4), sustituimos x = 2 en la derivada: dy/dx = 2(2) = 4 Entonces, la pendiente de la recta tangente en P(2, 4) es 4. Usando la forma punto-pendiente de una ecuación lineal, que es y - y1 = m(x - x1), donde (x1, y1) es un punto en la recta y m es la pendiente, podemos sustituir los valores de P( 2, 4) y la pendiente m = 4: y - 4 = 4(x - 2) Simplificando aún más: y - 4 = 4x - 8 Finalmente, podemos reordenar la ecuación para obtener la forma estándar: y = 4x - 4 Por lo tanto, la ecuación de la recta tangente a la curva de la función y = x^2 en el punto P(2, 4) es y = 4x - 4.

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