Let f be the function with derivative given by f'(x) = sin(x^2 + 1). How many relative extrema does f have on the interval 2 < x < 4 ? How would I solve this without a calculator?

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25-11-2016
Mathematics

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Let f be the function with derivative given by f'(x) = sin(x^2 + 1). How many relative extrema does f have on the interval 2 < x < 4 ? How would I solve this without a calculator?

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Аноним Аноним · Answer 1 · 2016-11-27T10:14:38+01:00

To find the extrema, set the derivative sin(x^2 + 1) equal to zero and solve for x. Each x and its corresponding f(x) value is the coordinate of an extrema. To find whether it is a max or a min, find the 2nd derivative and do the same thing. I believe a positive 2nd derivative is a min and a negative one is a max. Graph it to make sure.

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