What is the tangent of f(x)=7-x^2 ?

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

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tangent of f(x)=7-x^2

tangent of

f (x) = 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

f (x) = 7 - x^{2} : \frac{df ( x )}{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}

\int_{0}^{20} 1

\int 5 x^{2} sin (π x) d x

\frac{d}{d x} (ln ∣ x + 1 ∣)

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

\frac{d}{d x} (\frac{x - 4}{3 x - x ^{2}})

What is the tangent of f(x)=7-x^2 ?
The tangent of f(x)=7-x^2 is y=-2a_{0}x+7+a_{0}^2