What is the tangent of y=x^4 ?

The tangent of y=x^4 is y=4a_{0}^3x-3a_{0}^4

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tangent of y=x^4

tangent of

y = x^{4}

y = 4 a_{0}^{3} x - 3 a_{0}^{4}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{4})

Find the slope of

y = x^{4} : \frac{d y}{d x} = 4 x^{3}

Compute the slope of

y = x^{4}

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

Find the line with slope m=

4 a_{0}^{3}

and passing through

(a_{0}, a_{0}^{4}) : y = 4 a_{0}^{3} x - 3 a_{0}^{4}

y = 4 a_{0}^{3} x - 3 a_{0}^{4}

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