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How to find relative maximum from derivative graph

The relative maxima and minima can be found by differentiating the function and finding the turning points at which the slope is zero. Further, these turning points can be checked through

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Worked example: finding relative extrema

Key Steps. Find the possible maximums and minimums by identifying the x-intercepts of f ‘. The x -intercepts of f ’ ( x) are -2 and 4. Identify the intervals where f ‘ is above the x-axis and below

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Maximum and Minimum

The second derivative is y'' = 30x + 4. At x = −3/5: y'' = 30 (−3/5) + 4 = −14. it is less than 0, so −3/5 is a local maximum. At x = +1/3: y'' = 30 (+1/3) + 4 = +14. it is greater than 0, so +1/3 is a local minimum. (Now you can look at the graph.)

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Finding relative extrema (first derivative test)

To find relative maximums, we need to find where our first derivative changes sign. To do this, find your first derivative and then find where it is equal to zero. Begin with: at This means we have extrema at x=0 and x=-8/3. Because we are
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How to Find Local Extrema with the First Derivative Test

If the slope of f (x) is positive, then the graph of f’ (x) will be above the x-axis. All relative extrema of f (x) will become x-intercepts of f’ (x). All points of intersection of f (x) will become relative extrema of f’ (x). Additionally, if f (x)

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Relative minima & maxima review (article)

If x = y 2 12 and y = − 6, then x = 3 and z = f ( 3, − 6) = − 54. So, our three critical points are ( 0, 0, 0), ( 3, 6, – 54), and ( 3, – 6, – 54) Now it’s time to find our D-equation. D = f x x

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