Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 4x^3 - 6x^2 - 24x + 3, [-2, 3] absolute minimum value absolute maximum value
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The derivative of the function \(f(x) = 4x^3 - 6x^2 - 24x + 3\) is: \[f'(x) = 12x^2 - 12x - 24\] Setting \(f'(x) = 0\), we get: \[12x^2 - 12x - 24 = 0\] \[4x^2 - 4x - 8 = 0\] \[x^2 - x - 2 = 0\] \[(x - 2)(x + 1) = 0\] So, the critical points are \(x = 2\) and Show more…
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