What is the tangent of y=7-x^2 ?

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

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tangent of y=7-x^2

tangent of

y = 7 - x^{2}

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

y = 7 - x^{2}

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

Find the line with slope m=

- 2 a_{0}

and passing through

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

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

y = (1 - x) (x^{2} - 8)^{2}, (3, - 2)

\frac{d x}{d t} = - x - x^{2}

ln (3 x + 2)

n \to \infty lim (i = 1 \sum n \frac{i ^{3}}{n ^{4}} + \frac{1}{n})

m (t) = 5 t (3 t^{4} - 1)^{5}