When is the function f(x) = 3x^2 - 18x -100 at the lowest value

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The extreme values of any function f(x) lie at the solution of the equation f'(x) = 0. If the solution is x = a and f''(a) is positive, this is a minimum value and if f''(a) is negative this is a maximum value.

For f(x) = 3x^2 - 18x - 100, f'(x) = 6x - 18

6x - 18 = 0

=> x = 3

f''(x) = 6 which is always positive.

The lowest value of f(x) lies at x = 3.

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