What is the tangent of f(x)=x^4,\at x=3 ?

The tangent of f(x)=x^4,\at x=3 is y=108x-243

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tangent of f(x)=x^4,\at x=3

tangent of

f (x) = x^{4}, at x = 3

y = 108 x - 243

Solution steps

Find the tangent point:

(3, 81)

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 = 3 : m = 108

Find the line with slope m=

108

and passing through

(3, 81) : y = 108 x - 243

y = 108 x - 243

\int 1 + (\frac{x}{2} - 4)^{2} d x

\int 3 + 2 cos (x) d x

θ \to 0 lim (\frac{sin ( 3 θ )}{θ})

x \to 3 lim (\frac{x ^{2}}{x ^{2} - 9})

4 x + y^{2} = 12, x = y

What is the tangent of f(x)=x^4,\at x=3 ?
The tangent of f(x)=x^4,\at x=3 is y=108x-243