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Find an equation of the tangent line to the graph of f at the point (2, f(2)), where f(x) = (16 - 6x^2)^(-2/3).

User Dasqueel
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Final answer:

The equation of the tangent line to the graph of f(x) at (2, f(2)) is found by differentiating f(x) to get the slope at x = 2, and then using the point-slope form with this slope and the point (2, f(2)).

Step-by-step explanation:

To find an equation of the tangent line to the graph of function f at the point (2, f(2)), where f(x) = (16 - 6x2)(-2/3), we first need to calculate the derivative of f(x) to find the slope at x = 2. Then, we evaluate the derivative at x = 2 to get the slope of the tangent line.

The derivative, f'(x), gives us the slope at any point x on the curve. The slope of the tangent line at x = 2 is f'(2). Finally, we can use the point-slope form of a line to write the equation of the tangent. If f'(2) = m and f(2) = b, then the equation of the tangent line is y - b = m(x - 2).

User Osama
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