What is the tangent of 5x^2-7x ?

The tangent of 5x^2-7x is y=(10a_{0}-7)x-5a_{0}^2

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tangent of 5x^2-7x

tangent of

5 x^{2} - 7 x

y = (10 a_{0} - 7) x - 5 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 5 a_{0}^{2} - 7 a_{0})

Find the slope of

y = 5 x^{2} - 7 x : \frac{d y}{d x} = 10 x - 7

Compute the slope of

y = 5 x^{2} - 7 x

x = a_{0} : m = 10 a_{0} - 7

Find the line with slope m=

10 a_{0} - 7

and passing through

(a_{0}, 5 a_{0}^{2} - 7 a_{0}) : y = (10 a_{0} - 7) x - 5 a_{0}^{2}

y = (10 a_{0} - 7) x - 5 a_{0}^{2}

\frac{d}{d x} (a \cdot x \cdot e^{b x})

\int \frac{y - 1}{- y - 1} d y

\frac{\partial}{\partial y} (2 (y + 1) e^{2 x})

(- 6, 3), (4, - 1)

- 19.6 x + 2

What is the tangent of 5x^2-7x ?
The tangent of 5x^2-7x is y=(10a_{0}-7)x-5a_{0}^2