What is the tangent of f(x)=3x^2 ?

The tangent of f(x)=3x^2 is y=6a_{0}x-3a_{0}^2

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tangent of f(x)=3x^2

tangent of

f (x) = 3 x^{2}

y = 6 a_{0} x - 3 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

f (x) = 3 x^{2} : \frac{df ( x )}{d x} = 6 x

Compute the slope of

f (x) = 3 x^{2}

x = a_{0} : m = 6 a_{0}

Find the line with slope m=

6 a_{0}

and passing through

(a_{0}, 3 a_{0}^{2}) : y = 6 a_{0} x - 3 a_{0}^{2}

y = 6 a_{0} x - 3 a_{0}^{2}

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{x}}{1 + x ^{2}}

\int_{0}^{2} x + 2 d x

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

\frac{\partial}{\partial z} (x e^{6 y} sin (5 z))

\int e^{x^{\frac{1}{2}}} d x

What is the tangent of f(x)=3x^2 ?
The tangent of f(x)=3x^2 is y=6a_{0}x-3a_{0}^2