# What does the first derivative test tell you?

Growing or decreasing intervals of function and stationary points

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The first derivative test is used to determine whether a point on a function is a local maximum, local minimum, or neither. If the derivative of a function changes from positive to negative at a point, that point is a local maximum. If the derivative changes from negative to positive at a point, that point is a local minimum. If the derivative does not change sign (from positive to negative or negative to positive) around a point, then that point is neither a local maximum nor a local minimum.

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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 graph #F(x,y)=sqrt(x^2+y^2-1)+ln(4-x^2-y^2)#?
- How do you use the first and second derivatives to sketch # f(x) = (x+1)e^x#?
- How do I solve for the points of inflection involving trig functions?
- How do you find the first and second derivative of #ln (x^8)/ x^2#?
- How do you find all local maximum and minimum points using the second derivative test given #y=x^3-9x^2+24x#?

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