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angelinaangeli3
@angelinaangeli3
August 2022
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ПОЖАЛУЙСТА!!! ПОМОГИТЕ!!!
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oganesbagoyan
Verified answer
2)
y=4x/(4+x²) ;
y ' = (4x/(4+x²))' =4(x'(4+x²) -x(4+x²)' )/(4+x²)² =4(1*(4+x²)-x*2x)/(4+x²)² =
=4(4-x²)/((4+x²)² =4/(4+x²)²*(2+x)(2-x);
y'=0 ⇒ x₁=-2; x₂=2.
y ' -----------" -" ------- (-2) ------- " +" --------- (+2) ------ " -" -----------------
y ↓ ↑ ↓
Ф
ункция убивает x ∈(-∞; -2) и x∈ (2; ∞) ;
возрастает x
∈ (-2; 2)
x = -2
точка минимума ⇒
minf(x)
= f(-2) = 4*(-2)/(4 +(-2)²) =-8/8
= -1;
x = 2
точка максимума
maxf(x)
=f(2)=4*2)/(4 +2²) =-8/8
= 1;
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angelinaangeli3
Спасибо!
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Answers & Comments
Verified answer
2) y=4x/(4+x²) ;y ' = (4x/(4+x²))' =4(x'(4+x²) -x(4+x²)' )/(4+x²)² =4(1*(4+x²)-x*2x)/(4+x²)² =
=4(4-x²)/((4+x²)² =4/(4+x²)²*(2+x)(2-x);
y'=0 ⇒ x₁=-2; x₂=2.
y ' -----------" -" ------- (-2) ------- " +" --------- (+2) ------ " -" -----------------
y ↓ ↑ ↓
Функция убивает x ∈(-∞; -2) и x∈ (2; ∞) ;
возрастает x ∈ (-2; 2)
x = -2 точка минимума ⇒ minf(x) = f(-2) = 4*(-2)/(4 +(-2)²) =-8/8= -1;
x = 2 точка максимума maxf(x) =f(2)=4*2)/(4 +2²) =-8/8= 1;