What is the tangent of F(x)=x^4-8x^2+2 ?

The tangent of F(x)=x^4-8x^2+2 is y=(4a_{0}^3-16a_{0})x-3a_{0}^4+8a_{0}^2+2

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tangent of F(x)=x^4-8x^2+2

tangent of

F (x) = x^{4} - 8 x^{2} + 2

y = (4 a_{0}^{3} - 16 a_{0}) x - 3 a_{0}^{4} + 8 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}^{4} - 8 a_{0}^{2} + 2)

Find the slope of

F (x) = x^{4} - 8 x^{2} + 2 : \frac{d F ( x )}{d x} = 4 x^{3} - 16 x

Compute the slope of

F (x) = x^{4} - 8 x^{2} + 2

x = a_{0} : m = 4 a_{0}^{3} - 16 a_{0}

Find the line with slope m=

4 a_{0}^{3} - 16 a_{0}

and passing through

(a_{0}, a_{0}^{4} - 8 a_{0}^{2} + 2) : y = (4 a_{0}^{3} - 16 a_{0}) x - 3 a_{0}^{4} + 8 a_{0}^{2} + 2

y = (4 a_{0}^{3} - 16 a_{0}) x - 3 a_{0}^{4} + 8 a_{0}^{2} + 2

x \to 2 lim (n x + 2)

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

x \to 2 lim (x^{2} - 4)

\int 2 x + 2 d x

\frac{d}{d x} (x^{4 s i n (x)})

What is the tangent of F(x)=x^4-8x^2+2 ?
The tangent of F(x)=x^4-8x^2+2 is y=(4a_{0}^3-16a_{0})x-3a_{0}^4+8a_{0}^2+2