Find the points of local maxima or local minima and corresponding local maximum and local minimum values of functions. Also, find the points of inflection f(x) = x4 – 62x2 + 120x + 9

Asked by Sakshi | 1 year ago |  146

##### Solution :-

Given f (x) = x4 – 62x2 + 120x + 9

∴ f'(x) = 4x3 – 124x + 120 = 4(x3 – 31x + 30)

f”(x) = 12x2 – 124 = 4(3x2 – 31)

For maxima and minima, f'(x) = 0

4(x3 – 31x + 30) = 0

So roots will be x = 5, 1, – 6

Now, f”(5) = 176 > 0

x = 5 is point of local minima

f”(1) = – 112 < 0

x = 1 is point of local maxima

f”(– 6) = 308 > 0

x = – 6 is point of local minima

Local max value = f (1) = 68

Answered by Aaryan | 1 year ago

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