What is the tangent of y=x^3+3x^2+2 ?

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

Popular >

tangent of y=x^3+3x^2+2

tangent of

y = x^{3} + 3 x^{2} + 2

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = x^{3} + 3 x^{2} + 2 : \frac{d y}{d x} = 3 x^{2} + 6 x

Compute the slope of

y = x^{3} + 3 x^{2} + 2

x = a_{0} : m = 3 a_{0}^{2} + 6 a_{0}

Find the line with slope m=

3 a_{0}^{2} + 6 a_{0}

and passing through

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

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

\frac{d}{d x} \frac{e ^{- t}}{( x ^{2} + y ( t , x ) ^{2} ) ^{2}}

\int \frac{sec ^{2} ( x )}{tan ^{4} ( x )} d x

y^{^{'}} + x y = x y^{2}

\int_{a}^{b} \frac{1}{x ^{3}} d x

f (x) 50 - x

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