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Matematika - LS 24/25

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Spočtěte f ' (-5), když f(x)=(6x²-8)/(x-2).

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Na vhodném intervalu zderivujte funkci f(x)=\frac{x^3}{3}-\sqrt{5}.f(x)=\frac{x^3}{3}-\sqrt{5}.
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Spočtěte hodnotu f ' (-2), když f(x)=x^3+3x^2-7x+8f(x)=x^3+3x^2-7x+8
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Určete definiční obor funkce

f(x)=\textrm{arccos}(\frac{x}{4}+6).f(x)=\textrm{arccos}(\frac{x}{4}+6).
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Nalezněte definiční obor funkce dané předpisem f(x)=\sqrt{x^2-x-12}.f(x)=\sqrt{x^2-x-12}.

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Určete definiční obor funkce

f(x)=\ln(\frac{3x+9}{8-2x})+\ln(8).f(x)=\ln(\frac{3x+9}{8-2x})+\ln(8).
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Vyřešte nerovnici

\frac{-4x-4}{2x-6}\leq -1.\frac{-4x-4}{2x-6}\leq -1.
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Vyřešte nerovnici

6x^2-24x+26 < 8.6x^2-24x+26 < 8.
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Vypočtěte nejmenší reálné číslo, které je řešením soustavy nerovnic

8 ≤ 2 - 9x ≤ 15. Zaokrouhlete na dvě desetinná místa.

 

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