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) = x3 – 6x2 + 9x + 15

Asked by Sakshi | 1 year ago |  110

##### Solution :-

Given f (x) = x3 – 6x2 + 9x + 15

Differentiating f with respect to x

∴ f'(x) = 3x2 – 12x + 9 = 3(x2 – 4x + 3)

f” (x) = 6x – 12 = 6(x – 2)

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

3(x2 – 4x + 3) = 0

So roots will be x = 3, 1

Now, f” (3) = 6 > 0

x = 3 is point of local minima

f”(1) = – 6 < 0

x = 1 is point of local maxima

Local max value = f (1) = 19 and local min value = f (3) = 15

Answered by Aaryan | 1 year ago

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