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Mathematics 76 Online
OpenStudy (anonymous):

f(x) = 7 x^2 - 4 x. Find all extreme values (if any) of f and determine the values of x at which these values occur.

OpenStudy (anonymous):

1) Find the derivative \[f(x) = 7x ^{2}-4x\] \[f'(x) = 14x - 4\] 2) Set the derivative = 0 to find the critical points \[14x-4 = 0\] \[x = 2/7\] 3) Set up your intervals to determine increasing/decreasing \[(-\infty, 2/7) and (2/7, \infty)\] 3a) Find a test point in each interval and substitute into your first derivative to determine if increasing or decreasing. If you get from increasing to decreasing, you have a max. If you get from decreasing to increasing, you have a min. In the first interval, you get a negative (which means the graph is decreasing from -infinity to 2/7). For the second interval, you get a positive (which means the graph is increasing from 2/7 to infinity). Therefore, this means you have a minimum at x = 2/7. If you'd like to know the y-coordinate, simply plug in 2/7 in for x into your original function. Hope this helps! Good luck!

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