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Linear Approximation at a point
- Find a point you know to approximate to what they are asking.
- This point will be x1, plug in in original equation to get y1
- Take derivative of OG equation and plug in x1 to get slope
- Plug in for slope-int form, which is L(x)
- The x there will be the original X of the problem, so plug in to see the value of the Approximation and how close it was
Finding Local Extrema
- Take derivative of OG equation
- Set it equal to 0
- Solve for X to find critical points
- Use 2nd derivative, plug in crit points and see what sign they are
- if >0, local min at that point with value of the number plugged into OG equation
if <0, local max at that point with value of the number plugged into OG equation
Inflection points & Global max
- Inflection point = Where second derivative equals 0
- For global extrema, check the interval and see if the crit points of the function fit there. If so, plug in those numbers in the OG equation.
- The greatest number = global max at that point
- The lowest number = global min at that point
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