What is the tangent of f(x)=x^4 ?

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

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tangent of f(x)=x^4

tangent of

f (x) = 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

f (x) = x^{4} : \frac{df ( x )}{d x} = 4 x^{3}

Compute the slope of

f (x) = 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}

\frac{d}{d t} (- 5 sin (t))

y = x + \frac{2}{x}, (2, 3)

\int t^{4} e^{- t^{5}} d t

\frac{d ^{2}}{d x ^{2}} (- e^{- x^{2}})

\frac{\partial}{\partial x} (A x + B y + C x^{2} y)

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