What is the tangent of f(x)=9x-2x^2 ?

The tangent of f(x)=9x-2x^2 is y=(9-4a_{0})x+2a_{0}^2

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tangent of f(x)=9x-2x^2

tangent of

f (x) = 9 x - 2 x^{2}

y = (9 - 4 a_{0}) x + 2 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 9 a_{0} - 2 a_{0}^{2})

Find the slope of

f (x) = 9 x - 2 x^{2} : \frac{df ( x )}{d x} = 9 - 4 x

Compute the slope of

f (x) = 9 x - 2 x^{2}

x = a_{0} : m = 9 - 4 a_{0}

Find the line with slope m=

9 - 4 a_{0}

and passing through

(a_{0}, 9 a_{0} - 2 a_{0}^{2}) : y = (9 - 4 a_{0}) x + 2 a_{0}^{2}

y = (9 - 4 a_{0}) x + 2 a_{0}^{2}

\int \frac{1}{2 - ( x - 1 ) ^{2}} d x

\frac{d y}{d x} = k y (1 - y)

\int \frac{x ^{2} - 22}{x ^{3} - 2 x ^{2} + x} d x

x 8^{x}

\int 9 e^{- 9 x} sin (9 x) d x

What is the tangent of f(x)=9x-2x^2 ?
The tangent of f(x)=9x-2x^2 is y=(9-4a_{0})x+2a_{0}^2