Find the points of local maxima or local minima, if any, of the functi

1.	Find the points of local maxima or local minima, if any, of the functions, using the first derivative test. Also, find the local maximum or local minimum values, as the case may be: f(x) = 1/(x2 + 2)
Answer» Given as f(x) = 1/(x² + 2) Differentiate the above with respect to x f'(x) = -2x/(x² + 2)² For the local minima and local maxima, f'(x) = 0 -2x/(x² + 2)² = 0 So, x = 0, now for the values close to x = 0 and to the left of 0, f'(x) > 0 Also for the values x = 0 and to the right of 0, f’(x) < 0 So, by first derivative test, x = 0 is a point of local maxima and local minima value of f (x) is 1/2.

Find the points of local maxima or local minima, if any, of the functions, using the first derivative test. Also, find the local maximum or local minimum values, as the case may be: f(x) = 1/(x2 + 2)

Answer»

Given as f(x) = 1/(x² + 2)

Differentiate the above with respect to x

f'(x) = -2x/(x² + 2)²

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

-2x/(x² + 2)² = 0

So, x = 0, now for the values close to x = 0 and to the left of 0, f'(x) > 0

Also for the values x = 0 and to the right of 0, f’(x) < 0

So, by first derivative test, x = 0 is a point of local maxima and local minima value of f (x) is 1/2.