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

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jesuhlocun103 | Student, College Freshman | (Level 1) Honors

Posted February 14, 2013 at 8:55 PM via web

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

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted February 15, 2013 at 5:52 AM (Answer #1)

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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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