What is the tangent of 7x^2-3x ?

The tangent of 7x^2-3x is y=(14a_{0}-3)x-7a_{0}^2

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tangent of 7x^2-3x

tangent of

7 x^{2} - 3 x

y = (14 a_{0} - 3) x - 7 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 7 a_{0}^{2} - 3 a_{0})

Find the slope of

y = 7 x^{2} - 3 x : \frac{d y}{d x} = 14 x - 3

Compute the slope of

y = 7 x^{2} - 3 x

x = a_{0} : m = 14 a_{0} - 3

Find the line with slope m=

14 a_{0} - 3

and passing through

(a_{0}, 7 a_{0}^{2} - 3 a_{0}) : y = (14 a_{0} - 3) x - 7 a_{0}^{2}

y = (14 a_{0} - 3) x - 7 a_{0}^{2}

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What is the tangent of 7x^2-3x ?
The tangent of 7x^2-3x is y=(14a_{0}-3)x-7a_{0}^2