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in Derivatives by (50.7k points)
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Show that (x+1/x) has a maximum and minimum, but the maximum value is less than the minimum value

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Best answer

F(x) = x+1/x 

Taking first derivative and equating it to zero to find extreme points.

F’(x) = 1 - 1/x2 = 0

X= 1

x = 1, x = -1

now to determine which of these is min. And max. We use second derivative.

f || (x) = 2/x2

f || (1) = 2 and f || (-1) = -2

since f || (1) is +ve it is minimum point while f || (-1) is –ve it is maximum point

max value- > f(-1) = -1+1/-1 = -2

min value- > f(1) = 1+1/1 = 2

hence maximum value is less than minimum value

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