What is the first derivative test for local extreme values?
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The first derivative test for local extreme values states that if a function ( f(x) ) is continuous on an interval ( (a, b) ) and has a critical point at ( c ) in that interval:
- If ( f'(x) ) changes sign from positive to negative at ( c ), then ( f(c) ) is a local maximum.
- If ( f'(x) ) changes sign from negative to positive at ( c ), then ( f(c) ) is 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.
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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- Is the function concave up or down if #f(x)= (lnx)^2#?
- How do you find the first and second derivative of #(lnx)^3#?

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