What is the tangent of f^9 ?

The tangent of f^9 is y=9a_{0}^8f-8a_{0}^9

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tangent of f^9

tangent of

f^{9}

y = 9 a_{0}^{8} f - 8 a_{0}^{9}

Solution steps

Compute the tangent line to the general point

f = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{9})

Find the slope of

y = f^{9} : \frac{d y}{df} = 9 f^{8}

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 = 9 a_{0}^{8}

Find the line with slope m=

9 a_{0}^{8}

and passing through

(a_{0}, a_{0}^{9}) : y = 9 a_{0}^{8} f - 8 a_{0}^{9}

y = 9 a_{0}^{8} f - 8 a_{0}^{9}