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Find the tangent line for the graph of `y = x^4`  at ( 3 , 81 )

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Find the tangent line for the graph of `y = x^4`  at ( 3 , 81 )

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The equation of the tangent to the graph of y = x^4 at the point (3, 81) has to be determined.

The slope of the tangent to a point on the graph of y = f(x) at x = a is equal to f'(a).

For y = x^4

y' = 4x^3

At x = 3, y' = 4*27 = 108

The equation of the tangent is (y - 81)/(x - 3) = 108

=> y - 81 = 108x - 324

=> 108x - y - 243 = 0

The required equation of the tangent is 108x - y - 243 = 0

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