What is the tangent of x^2-7 ?

The tangent of x^2-7 is y=2a_{0}x-a_{0}^2-7

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tangent of x^2-7

tangent of

x^{2} - 7

y = 2 a_{0} x - a_{0}^{2} - 7

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{2} - 7)

Find the slope of

y = x^{2} - 7 : \frac{d y}{d x} = 2 x

Compute the slope of

y = x^{2} - 7

x = a_{0} : m = 2 a_{0}

Find the line with slope m=

2 a_{0}

and passing through

(a_{0}, a_{0}^{2} - 7) : y = 2 a_{0} x - a_{0}^{2} - 7

y = 2 a_{0} x - a_{0}^{2} - 7

\frac{y ^{^{'}}}{y} = 6 x^{2}

\frac{d y}{d x}, y \cdot cos (x) = 2 x^{2} + 5 y^{2}

\int_{5}^{8} \frac{x}{x ^{2} + 6 x + 13} d x

\int_{\frac{1}{7}}^{5} 14 x ln (7 x) d x

f (x) = (x + 1) (x^{3} + x - 2)