What is the tangent of 7-x^2 ?

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

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tangent of 7-x^2

tangent of

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

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

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

(ln (x))^{6}

x \to 7 lim (\frac{∣ 7 - x ∣}{7 - x})

\int \frac{x ^{3}}{e ^{2 x}} d x

\frac{d x}{d t} = - 1 + (x + t - 1)^{2}

\int \frac{e ^{2 x}}{1 - e ^{2 x}} d x