What is the tangent of f(x)=2x^3+3x^2-12x+7 ?

The tangent of f(x)=2x^3+3x^2-12x+7 is y=(6a_{0}^2+6a_{0}-12)x-4a_{0}^3-3a_{0}^2+7

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tangent of f(x)=2x^3+3x^2-12x+7

tangent of

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 7

y = (6 a_{0}^{2} + 6 a_{0} - 12) x - 4 a_{0}^{3} - 3 a_{0}^{2} + 7

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 a_{0}^{3} + 3 a_{0}^{2} - 12 a_{0} + 7)

Find the slope of

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 7 : \frac{df ( x )}{d x} = 6 x^{2} + 6 x - 12

Compute the slope of

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 7

x = a_{0} : m = 6 a_{0}^{2} + 6 a_{0} - 12

Find the line with slope m=

6 a_{0}^{2} + 6 a_{0} - 12

and passing through

(a_{0}, 2 a_{0}^{3} + 3 a_{0}^{2} - 12 a_{0} + 7) : y = (6 a_{0}^{2} + 6 a_{0} - 12) x - 4 a_{0}^{3} - 3 a_{0}^{2} + 7

y = (6 a_{0}^{2} + 6 a_{0} - 12) x - 4 a_{0}^{3} - 3 a_{0}^{2} + 7

x \to \infty lim (- 10 e^{- 2 x})

\frac{d y}{d t} = \frac{y}{2}

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

\frac{d}{d x} (\frac{e ^{x}}{6 x ^{2} + 1})

What is the tangent of f(x)=2x^3+3x^2-12x+7 ?
The tangent of f(x)=2x^3+3x^2-12x+7 is y=(6a_{0}^2+6a_{0}-12)x-4a_{0}^3-3a_{0}^2+7