g-x-x-2-1-ln-x-Study-the-variations-of-the-function-g-and-draw-up-its-table-of-variations-

Question Number 171284 by Kodjo last updated on 11/Jun/22

g (x) = - x^{2} + 1 - l n ∣ x ∣

Study the variations of the function g and draw up its table of variations

Answered by a.lgnaoui last updated on 12/Jun/22

Answered by a.lgnaoui last updated on 12/Jun/22

p o u r x < 0 g (x) = x^{2} + 1 - l n (- x)

g^{'} (x) = 2 x + \frac{1}{x} = \frac{2 x^{2} + 1}{x} < 0 g (x) d e c r o i s s a n t

x - \infty 0

+ \infty ∖ - \infty

l i m g {(x)}_{x \to - \infty} = 2 x - \frac{1}{- x} = 2 x + \frac{1}{x} = + \infty

l i m g {(x)}_{x \to - 0} = - \infty