Find an equation of the tangent line to the graph of f(x)=`2/root(4)(x^3)`



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Posted on (Answer #1)

The function `f(x) = 2/root(4)(x^3) = 2/x^(3/4)`

The equation of the tangent to the graph of f(x) at a point (X, f(X)) is given by: `(y - f(X))/(x - X) = f'(X)`

=> `(y - f(X))/(x - X) = 2*(-3/4)*X^(-7/4) = (-3/2)*X^(-7/4)`

=> `(y - 2/X^(3/4))/(x - X) = (-3/2)*X^(-7/4)`

The equation of the tangent at any point `(X, f(X))` is `(y - 2/X^(3/4))/(x - X) = (-3/2)*X^(-7/4)`

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