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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