# How do you find the exact relative maximum and minimum of the polynomial function of #f(x)=2x^3+3x^2-12x #?

Relative maximum:

Relative minimum:

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To find the exact relative maximum and minimum of the polynomial function f(x) = 2x^3 + 3x^2 - 12x, you would first find the critical points by setting the derivative equal to zero and solving for x. Next, evaluate the second derivative at these critical points to determine the nature of the extremum (maximum or minimum). If the second derivative is positive, it's a relative minimum; if it's negative, it's a relative maximum. If the second derivative is zero or undefined, the test is inconclusive, and you would need to use other methods like the first derivative test or analyze the function graphically.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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