What is the tangent of f(x)=x^4-17x^2+16 ?

The tangent of f(x)=x^4-17x^2+16 is y=(4a_{0}^3-34a_{0})x-3a_{0}^4+17a_{0}^2+16

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tangent of f(x)=x^4-17x^2+16

tangent of

f (x) = x^{4} - 17 x^{2} + 16

y = (4 a_{0}^{3} - 34 a_{0}) x - 3 a_{0}^{4} + 17 a_{0}^{2} + 16

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{4} - 17 a_{0}^{2} + 16)

Find the slope of

f (x) = x^{4} - 17 x^{2} + 16 : \frac{df ( x )}{d x} = 4 x^{3} - 34 x

Compute the slope of

f (x) = x^{4} - 17 x^{2} + 16

x = a_{0} : m = 4 a_{0}^{3} - 34 a_{0}

Find the line with slope m=

4 a_{0}^{3} - 34 a_{0}

and passing through

(a_{0}, a_{0}^{4} - 17 a_{0}^{2} + 16) : y = (4 a_{0}^{3} - 34 a_{0}) x - 3 a_{0}^{4} + 17 a_{0}^{2} + 16

y = (4 a_{0}^{3} - 34 a_{0}) x - 3 a_{0}^{4} + 17 a_{0}^{2} + 16

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What is the tangent of f(x)=x^4-17x^2+16 ?
The tangent of f(x)=x^4-17x^2+16 is y=(4a_{0}^3-34a_{0})x-3a_{0}^4+17a_{0}^2+16