What is the tangent of f(x)=x^2-1/x ,(-1,0) ?

The tangent of f(x)=x^2-1/x ,(-1,0) is y=4.40366…x+4.40366… \lor y=-4.40366…x-4.40366…

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tangent of f(x)=x^2-1/x ,(-1,0)

tangent of

f (x) = x^{2} - \frac{1}{x}, (- 1, 0)

y = 4.40366 \dots x + 4.40366 \dots or y = - 4.40366 \dots x - 4.40366 \dots

Solution steps

Slope of the tangent line at

(- 1, 0) : m = \frac{x ^{3} - 1}{x ( x + 1 )}

Find the slope of

f (x) = x^{2} - \frac{1}{x} : m = 2 x + \frac{1}{x ^{2}}

Solve

2 x + \frac{1}{x ^{2}} = \frac{x ^{3} - 1}{x ( x + 1 )} : x \approx - 0.43542 \dots, x \approx - 2.29663 \dots

Find the tangent line at

x = - 0.43542 \dots : y = 4.40366 \dots x + 4.40366 \dots

Find the tangent line at

x = - 2.29663 \dots : y = - 4.40366 \dots x - 4.40366 \dots

y = 4.40366 \dots x + 4.40366 \dots or y = - 4.40366 \dots x - 4.40366 \dots

\int_{0}^{2} \frac{x + 2}{x - 4} d x

x^{\frac{2}{3}}

\frac{d}{d x} ((x^{3} + 2 x)^{37})

\frac{\partial}{\partial y} (x^{3} y^{4} + x^{4} y^{3})

\frac{d}{d x} (- \frac{10 x}{( x ^{2} - 9 ) ^{2}})

What is the tangent of f(x)=x^2-1/x ,(-1,0) ?
The tangent of f(x)=x^2-1/x ,(-1,0) is y=4.40366…x+4.40366… \lor y=-4.40366…x-4.40366…