What is the tangent of x^4-25x^2+144 ?

The tangent of x^4-25x^2+144 is y=(4a_{0}^3-50a_{0})x-3a_{0}^4+25a_{0}^2+144

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tangent of x^4-25x^2+144

tangent of

x^{4} - 25 x^{2} + 144

y = (4 a_{0}^{3} - 50 a_{0}) x - 3 a_{0}^{4} + 25 a_{0}^{2} + 144

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{4} - 25 a_{0}^{2} + 144)

Find the slope of

y = x^{4} - 25 x^{2} + 144 : \frac{d y}{d x} = 4 x^{3} - 50 x

Compute the slope of

y = x^{4} - 25 x^{2} + 144

x = a_{0} : m = 4 a_{0}^{3} - 50 a_{0}

Find the line with slope m=

4 a_{0}^{3} - 50 a_{0}

and passing through

(a_{0}, a_{0}^{4} - 25 a_{0}^{2} + 144) : y = (4 a_{0}^{3} - 50 a_{0}) x - 3 a_{0}^{4} + 25 a_{0}^{2} + 144

y = (4 a_{0}^{3} - 50 a_{0}) x - 3 a_{0}^{4} + 25 a_{0}^{2} + 144

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What is the tangent of x^4-25x^2+144 ?
The tangent of x^4-25x^2+144 is y=(4a_{0}^3-50a_{0})x-3a_{0}^4+25a_{0}^2+144