Question

Исследовать функцию на экстремум. 

 

f(x) = x^2+2 / 2x-1 

 

 

Answer 1

f '(x) = (2x(2x-1) - 2(x²+2)) / (2x-1)²
f '(x) = 0
(2x-1) ≠0
2x(2x-1) - 2(x²+2) = 0
4x² - 2x - 2x² - 4 = 0
2x² - 2x - 4 = 0
x₁ = -1
x₂ = 2
++++++++ [-1] ------(1/2)--- [2] +++++++
 Xmax = -1
Xmin = 2