What is the tangent of y=7x^2-4x,-74 ?

The tangent of y=7x^2-4x,-74 is y=(14a_{0}-4)x-7a_{0}^2

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tangent of y=7x^2-4x,-74

tangent of

y = 7 x^{2} - 4 x, - 74

y = (14 a_{0} - 4) 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} - 4 a_{0})

Find the slope of

y = 7 x^{2} - 4 x : \frac{d y}{d x} = 14 x - 4

Compute the slope of

y = 7 x^{2} - 4 x

x = a_{0} : m = 14 a_{0} - 4

Find the line with slope m=

14 a_{0} - 4

and passing through

(a_{0}, 7 a_{0}^{2} - 4 a_{0}) : y = (14 a_{0} - 4) x - 7 a_{0}^{2}

y = (14 a_{0} - 4) x - 7 a_{0}^{2}

\int (x - 9)^{2} d x

\int_{0}^{\frac{π}{3}} tan^{5} (x) d x

y^{^{''}} + \frac{6}{x} y^{^{'}} + \frac{4}{x ^{2}} y = 0

f (x) = x^{2} - 4 x + 2

x \to 1 lim (e^{(x^{3} - x)})

What is the tangent of y=7x^2-4x,-74 ?
The tangent of y=7x^2-4x,-74 is y=(14a_{0}-4)x-7a_{0}^2