How does the first derivative test work?
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The first derivative test is a method used to analyze critical points of a function to determine whether they correspond to local maxima, local minima, or saddle points. The test relies on the behavior of the function's derivative in the vicinity of these critical points. Specifically, if the derivative changes sign at a critical point from positive to negative, the point corresponds to a local maximum. If the derivative changes sign from negative to positive, the point corresponds to a local minimum. If the derivative does not change sign at the critical point, it indicates a saddle point.
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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.
- How do you find all points of inflection given #y=((x-3)/(x+1))^2#?
- How do you find the maximum or minimum of #f(x)=x^2+6x-2#?
- How do you sketch the graph #y=sinx+sin^2x# using the first and second derivatives from #0<=x<2pi#?
- For what values of x is #f(x)= x^4-3x^3-4x-7 # concave or convex?
- How do you determine whether the function #y=x^2 # is concave up or concave down and its intervals?

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