find-maximum-of-z-2-2z-3-

Question Number 197822 by mokys last updated on 30/Sep/23

f i n d m a x i m u m o f ∣ z^{2} + 2 z - 3 ∣ ?

Commented by AST last updated on 30/Sep/23

\infty

Commented by mokys last updated on 30/Sep/23

t h e a n s w e r i s \frac{8}{\sqrt{3}}

Commented by AST last updated on 30/Sep/23

M a x i m u m ?

Commented by mokys last updated on 30/Sep/23

y e s

Commented by AST last updated on 30/Sep/23

{W h a t}^{'} s f (10000000) ?

Answered by a.lgnaoui last updated on 30/Sep/23

{\begin{cases} f (z) = z^{2} + 2 z - 3 z \in] - \infty, - 3] [1 + \infty \\ f (z) = 3 - 2 z - z^{2} z \in [- 3, 1] \end{cases}

f^{^{'}} (z) = 0 z = - 1 \in [- 3, 1] \Rightarrow f (- 1) = 4

so the maximum relative is 4

Commented by a.lgnaoui last updated on 30/Sep/23

for f (z) = z^{2} + 2 z - 3 (z \in] - \infty, - 3] ⊔ [1, + \infty [)

the maximum absolu is + \infty

Commented by a.lgnaoui last updated on 30/Sep/23

Commented by mahdipoor last updated on 30/Sep/23

f (- 3) = f (1) = 0 i s a b s o l u t e m i n i m u m

f (- 1) = 4 i s l o c a l m a x i m u m

f (\pm \infty) = + \infty i s a b s o l u t e m a x i m u m