What is the tangent of f(x)=x^3-7x^2 ?

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

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tangent of f(x)=x^3-7x^2

tangent of

f (x) = x^{3} - 7 x^{2}

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

f (x) = x^{3} - 7 x^{2} : \frac{df ( x )}{d x} = 3 x^{2} - 14 x

Compute the slope of

f (x) = x^{3} - 7 x^{2}

x = a_{0} : m = 3 a_{0}^{2} - 14 a_{0}

Find the line with slope m=

3 a_{0}^{2} - 14 a_{0}

and passing through

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

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

\frac{d y}{d x} = (e^{x} + 10)^{2}

\frac{\partial}{\partial x} (\frac{( x - y )}{z})

\int (sin (x) e^{2 x}) d x

\frac{d}{d x} (sin (\frac{5}{x}))

\frac{\partial}{\partial x} (x cos (z))

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