1) f(x) =1/4x⁴-2x²;
f '(x) =(1/4x⁴-2x²)' = 3x³ - 4x;
f '(x) = 0; 3x³ - 4x = 0; x(3x² - 4) = 0;
x₁ = 0 або 3x² - 4 = 0
3x² = 4
x² = 4/3
x₂ = 2/√3; x₃ = -2/√3.
- - - - - +++++ - - - - - - ++++++
------------- -2/√3 ------------- 0 -------------- 2/√3 ---------------->
x∈ (-2/√3; 0) i x∈ (2/√3; ∝).
2) f(x)=1/5x⁵-3/2x²+2
f '(x) = (1/5x⁵-3/2x²+2)' = x⁴ - 3x²;
f '(x) = 0; x⁴ - 3x² = 0; x²(x² - 3) = 0;
x₁ = 0 або x² - 3 = 0;
x² = 3;
x₂ = -√3; x₃ = √3.
++++++ - - - - - - - - - - - - ++++++
------------- -√3 ------------- 0 -------------- √3 ---------------->
x∈ (-∝; -√3) i x∈ (√3; ∝).
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Answers & Comments
1) f(x) =1/4x⁴-2x²;
f '(x) =(1/4x⁴-2x²)' = 3x³ - 4x;
f '(x) = 0; 3x³ - 4x = 0; x(3x² - 4) = 0;
x₁ = 0 або 3x² - 4 = 0
3x² = 4
x² = 4/3
x₂ = 2/√3; x₃ = -2/√3.
- - - - - +++++ - - - - - - ++++++
------------- -2/√3 ------------- 0 -------------- 2/√3 ---------------->
x∈ (-2/√3; 0) i x∈ (2/√3; ∝).
2) f(x)=1/5x⁵-3/2x²+2
f '(x) = (1/5x⁵-3/2x²+2)' = x⁴ - 3x²;
f '(x) = 0; x⁴ - 3x² = 0; x²(x² - 3) = 0;
x₁ = 0 або x² - 3 = 0;
x² = 3;
x₂ = -√3; x₃ = √3.
++++++ - - - - - - - - - - - - ++++++
------------- -√3 ------------- 0 -------------- √3 ---------------->
x∈ (-∝; -√3) i x∈ (√3; ∝).