What is the tangent of x^2-4x+25 ?

The tangent of x^2-4x+25 is y=(2a_{0}-4)x-a_{0}^2+25

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tangent of x^2-4x+25

tangent of

x^{2} - 4 x + 25

y = (2 a_{0} - 4) x - a_{0}^{2} + 25

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{2} - 4 a_{0} + 25)

Find the slope of

y = x^{2} - 4 x + 25 : \frac{d y}{d x} = 2 x - 4

Compute the slope of

y = x^{2} - 4 x + 25

x = a_{0} : m = 2 a_{0} - 4

Find the line with slope m=

2 a_{0} - 4

and passing through

(a_{0}, a_{0}^{2} - 4 a_{0} + 25) : y = (2 a_{0} - 4) x - a_{0}^{2} + 25

y = (2 a_{0} - 4) x - a_{0}^{2} + 25

\frac{\partial}{\partial x} (830 x - \frac{25000}{x} - \frac{5400}{y} + 2280 y + 457950)

\frac{\partial}{\partial x} (e^{x} cos (y) - z)

\int \frac{x ^{3} + 1}{x ^{3} - x ^{2}} d x

\frac{d}{d y} (ln (y^{2}))

\int (\frac{x ^{3} + 7}{x ^{2}}) d x

What is the tangent of x^2-4x+25 ?
The tangent of x^2-4x+25 is y=(2a_{0}-4)x-a_{0}^2+25