What is the tangent of x^2-x ?

The tangent of x^2-x is y=(2a_{0}-1)x-a_{0}^2

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tangent of x^2-x

tangent of

x^{2} - x

y = (2 a_{0} - 1) 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} - a_{0})

Find the slope of

y = x^{2} - x : \frac{d y}{d x} = 2 x - 1

Compute the slope of

y = x^{2} - x

x = a_{0} : m = 2 a_{0} - 1

Find the line with slope m=

2 a_{0} - 1

and passing through

(a_{0}, a_{0}^{2} - a_{0}) : y = (2 a_{0} - 1) x - a_{0}^{2}

y = (2 a_{0} - 1) x - a_{0}^{2}

\frac{d x}{d t} - 4 x = cos (5 t)

f (x) = - 3 x^{3} - 2 x^{2} - x + 3, (-, 5)

n = 1 \sum \infty \frac{1}{n ^{7}}

\int sin (12 x) cos (9 x) d x

x \to 0 + lim (arctan (\frac{1}{x}))