What is the extreme value of 2x^3+3x^2-12x+5?

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The extreme values of a function occur at the points where the derivative is equal to 0.

f(x) = 2x^3 + 3x^2 - 12x + 5

=> f'(x) = 6x^2 + 6x - 12

6x^2 + 6x - 12 = 0

=> x^2 + x - 2 = 0

=>...

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The extreme values of a function occur at the points where the derivative is equal to 0.

f(x) = 2x^3 + 3x^2 - 12x + 5

=> f'(x) = 6x^2 + 6x - 12

6x^2 + 6x - 12 = 0

=> x^2 + x - 2 = 0

=> x^2 + 2x - x - 2 = 0

=> x(x + 2) - 1(x + 2) = 0

=> (x - 1)(x + 2) = 0

x = 1 and x = -2

f(x) = -2 for x = 1 and f(x) = 25 for x = -2.

The extreme values are x1 = -2 and x2 = 25.

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