How do you find the local max and min for f(x) = 7x + 9x^(-1)?

1 Answer
Nov 29, 2016

To find the local extrema we find the points where the first derivative is null and study the sign of the second derivative

Explanation:

f(x) =7x+9x^(-1)

f'(x) =7 -9x^(-2)

f''(x) =18x^(-3)

Find the values of x where f'(x)=0

7-9/x^2 = 0

7x^2-9 = 0

x=+-3/sqrt(7)

In both points f''(x) !=0 so these are local extrema, namely:

1) around x=-3/sqrt(7) the second derivative is negative and then the point is a local maximum.

2) around x=+3/sqrt(7) the second derivative is positive and then the point is a local minimum.

graph{7x+9/x [-47.3, 47.2, -73.6, 73.6]}