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

The tangent of 4x^2-2x+4 is y=(8a_{0}-2)x-4a_{0}^2+4

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tangent of 4x^2-2x+4

tangent of

4 x^{2} - 2 x + 4

y = (8 a_{0} - 2) x - 4 a_{0}^{2} + 4

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = 4 x^{2} - 2 x + 4 : \frac{d y}{d x} = 8 x - 2

Compute the slope of

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

x = a_{0} : m = 8 a_{0} - 2

Find the line with slope m=

8 a_{0} - 2

and passing through

(a_{0}, 4 a_{0}^{2} - 2 a_{0} + 4) : y = (8 a_{0} - 2) x - 4 a_{0}^{2} + 4

y = (8 a_{0} - 2) x - 4 a_{0}^{2} + 4

\frac{\partial}{\partial x} (3 x^{2} + 6 x y^{3})

7 - 4 t

\int_{0}^{1} 46 \frac{1}{x ^{p}} d x

\int \frac{1}{( 1 + 4 x ^{2} ) ^{\frac{3}{2}}} d x

\int \frac{8}{x ^{4}} d x

What is the tangent of 4x^2-2x+4 ?
The tangent of 4x^2-2x+4 is y=(8a_{0}-2)x-4a_{0}^2+4