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
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
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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math is the study of numbers, shapes, and patterns. It is used in everyday life, from counting to measuring to more complex calculations.
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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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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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