What is the tangent of f(x)=3x^2-3x,\at x=3 ?

The tangent of f(x)=3x^2-3x,\at x=3 is y=15x-27

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tangent of f(x)=3x^2-3x,\at x=3

tangent of

f (x) = 3 x^{2} - 3 x, at x = 3

y = 15 x - 27

Solution steps

Find the tangent point:

(3, 18)

Find the slope of

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

Compute the slope of

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

x = 3 : m = 15

Find the line with slope m=

15

and passing through

(3, 18) : y = 15 x - 27

y = 15 x - 27

x \to 0 lim (\frac{sinh ( x )}{x})

\frac{6 x ^{2} + 2 x + 4}{x}

y^{^{''}} + 3 y^{^{'}} - 2 y = 0

\frac{d y}{d x} = 4 e^{x - y}

(x y + y^{2} + y) d x + (x + 2 y) d y = 0

What is the tangent of f(x)=3x^2-3x,\at x=3 ?
The tangent of f(x)=3x^2-3x,\at x=3 is y=15x-27