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

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

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

tangent of

f (x) = - x^{2} + 7 x

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, - a_{0}^{2} + 7 a_{0})

Find the slope of

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

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} + 7

Find the line with slope m=

- 2 a_{0} + 7

and passing through

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

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

\int_{- 1}^{1} x^{3} - 6 x d x

x^{4} + 5 x^{2} - x

h (w) = \frac{w ^{2} - 1}{w ^{2} + 1}

\frac{d}{d x} (\frac{x ^{3}}{12})

\frac{1}{2} (9 t^{2} + t)^{- 3}

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