# How do I find the absolute minimum and maximum of a function using its derivatives?

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To find the absolute minimum and maximum of a function using its derivatives, follow these steps:

- Find the critical points of the function by setting its derivative equal to zero and solving for ( x ).
- Determine the intervals between the critical points.
- Evaluate the function at the critical points and at the endpoints of the intervals.
- The lowest function value among these values is the absolute minimum, and the highest function value is the absolute maximum.

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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.

- How do you find the intervals of increasing and decreasing using the first derivative given #y=(x^5-5x)/5#?
- How do you find the number c that satisfies the conclusion of the Mean Value Theorem for the function #f(x)=x^2 - 2x + 5# on the interval #[1, 3]#?
- What are the extrema of #f(x)=(x^2)/(x^2-3x)+8 # on #x in[4,9]#?
- How do you find the intervals of increasing and decreasing given #y=-x^3+2x^2+2#?
- How do you find the critical points for #f(x)= (2x^2+5x+5)/(x+1)#?

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