What is the tangent of 5-x^2 ?

The tangent of 5-x^2 is y=-2a_{0}x+5+a_{0}^2

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tangent of 5-x^2

tangent of

5 - x^{2}

y = - 2 a_{0} x + 5 + a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 5 - a_{0}^{2})

Find the slope of

y = 5 - x^{2} : \frac{d y}{d x} = - 2 x

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = - 2 a_{0}

Find the line with slope m=

- 2 a_{0}

and passing through

(a_{0}, 5 - a_{0}^{2}) : y = - 2 a_{0} x + 5 + a_{0}^{2}

y = - 2 a_{0} x + 5 + a_{0}^{2}

d er i v a t i v e f (x) = ln (x^{2} + 3)

d er i v a t i v e y = (x + 1) (x + 2)

x^{2} y^{^{'}} = y^{2} + 5 x y + 4 x^{2}

d er i v a t i v e x = t sin (t)

d er i v a t i v e 8 e^{t}