What is the tangent of f(x)=x^4-10x^2+9 ?

The tangent of f(x)=x^4-10x^2+9 is y=(4a_{0}^3-20a_{0})x-3a_{0}^4+10a_{0}^2+9

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tangent of f(x)=x^4-10x^2+9

tangent of

f (x) = x^{4} - 10 x^{2} + 9

y = (4 a_{0}^{3} - 20 a_{0}) x - 3 a_{0}^{4} + 10 a_{0}^{2} + 9

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{4} - 10 a_{0}^{2} + 9)

Find the slope of

f (x) = x^{4} - 10 x^{2} + 9 : \frac{df ( x )}{d x} = 4 x^{3} - 20 x

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = 4 a_{0}^{3} - 20 a_{0}

Find the line with slope m=

4 a_{0}^{3} - 20 a_{0}

and passing through

(a_{0}, a_{0}^{4} - 10 a_{0}^{2} + 9) : y = (4 a_{0}^{3} - 20 a_{0}) x - 3 a_{0}^{4} + 10 a_{0}^{2} + 9

y = (4 a_{0}^{3} - 20 a_{0}) x - 3 a_{0}^{4} + 10 a_{0}^{2} + 9

What is the tangent of f(x)=x^4-10x^2+9 ?
The tangent of f(x)=x^4-10x^2+9 is y=(4a_{0}^3-20a_{0})x-3a_{0}^4+10a_{0}^2+9