What is the tangent of f(x)=x^5-3(x)^3+6 ?

The tangent of f(x)=x^5-3(x)^3+6 is y=(5a_{0}^4-9a_{0}^2)x-4a_{0}^5+6a_{0}^3+6

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tangent of f(x)=x^5-3(x)^3+6

tangent of

f (x) = x^{5} - 3 (x)^{3} + 6

y = (5 a_{0}^{4} - 9 a_{0}^{2}) x - 4 a_{0}^{5} + 6 a_{0}^{3} + 6

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{5} - 3 a_{0}^{3} + 6)

Find the slope of

f (x) = x^{5} - 3 x^{3} + 6 : \frac{df ( x )}{d x} = 5 x^{4} - 9 x^{2}

Compute the slope of

f (x) = x^{5} - 3 x^{3} + 6

x = a_{0} : m = 5 a_{0}^{4} - 9 a_{0}^{2}

Find the line with slope m=

5 a_{0}^{4} - 9 a_{0}^{2}

and passing through

(a_{0}, a_{0}^{5} - 3 a_{0}^{3} + 6) : y = (5 a_{0}^{4} - 9 a_{0}^{2}) x - 4 a_{0}^{5} + 6 a_{0}^{3} + 6

y = (5 a_{0}^{4} - 9 a_{0}^{2}) x - 4 a_{0}^{5} + 6 a_{0}^{3} + 6

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What is the tangent of f(x)=x^5-3(x)^3+6 ?
The tangent of f(x)=x^5-3(x)^3+6 is y=(5a_{0}^4-9a_{0}^2)x-4a_{0}^5+6a_{0}^3+6