How do you find the exact relative maximum and minimum of the polynomial function of #y=x^3#?

Answer 1

#x in (-oo, oo)#. There are no extrema at all..

#y'=3x^2 and y'' ==x# are 0 at #x = 0. y'''= 6 > 0.#

So. y is neither a maximum nor a minimum at x = 0.

Note that y'' = 6x > 0 for x > 0 and < 0 for x < 0.

Origin is a point of inflexion wherein y'changes sign and the tangent

y = 0 crosses the curve..

Also, #x in (-oo, oo#) .
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Answer 2

To find the relative maximum and minimum of the polynomial function ( y = x^3 ), you first find its critical points by setting its derivative equal to zero. Then, you analyze the behavior of the function around these critical points using the first or second derivative test to determine whether they correspond to relative maximum, minimum, or neither. For ( y = x^3 ), there are no relative maximum or minimum points since it is a monotonic increasing function.

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Answer from HIX Tutor

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.

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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