electrochika
  • electrochika
If the derivative of f is given by f'(x) = e^x - 3x^2, at which of the following values of x does f have a relative maximum value? a. -0.46 b. 0.20 c. 0.91 d. 0.95 e. 3.73
Mathematics
chestercat
  • chestercat
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Rogue
  • Rogue
The easiest way to solve this problem would be to graph the derivative. When the derivative equals zero, f could possibly have a local minimum or maximum at that point. Upon graphing, you'll see that f' intersects the x-axis 3 times, at \[x = -0.459, x = 0.910, x= 3.733\] At the first and third points, the derivative changes signs from negative to positive. That means that f changes from decreasing to increasing, which would mean that those are local minima. At the middle point, f' changes from positive to negative, indicating that f changes from increasing to decreasing at that point. That would mean that the local maximum is at x = 0.91. Choice C.

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