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Matematika - LS 24/25

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Spočtěte hodnotu f ' (-2), když f(x)=x^3+3x^2+4x+7f(x)=x^3+3x^2+4x+7
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Určete definiční obor funkce

f(x)=\ln(\frac{-3x+9}{5-5x})+\ln(8).f(x)=\ln(\frac{-3x+9}{5-5x})+\ln(8).
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Vyřešte nerovnici

4x^2-24x+30 < -2.4x^2-24x+30 < -2.
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Vyřešte nerovnici

\frac{-3x-6}{2x-8}\geq -1.\frac{-3x-6}{2x-8}\geq -1.
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Vypočtěte největší reálné číslo, které je řešením soustavy nerovnic

9 ≤ 10 - 3x ≤ 17. Zaokrouhlete na dvě desetinná místa.

 

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Na vhodném intervalu zderivujte funkci f(x)=\frac{x^4}{4}-\sqrt{5}.f(x)=\frac{x^4}{4}-\sqrt{5}.
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Spočtěte hodnotu f ' (-5), když f(x)=(4x-9)/(x-1).

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Spočtěte derivaci dané funkce

f(x)=\frac{6x^2+7}{e^{9x}}.f(x)=\frac{6x^2+7}{e^{9x}}.
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Spočtěte hodnotu f ' (1), když f(x)=x^3-2x^2+5x-8f(x)=x^3-2x^2+5x-8
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Nalezněte definiční obor funkce dané předpisem f(x)=\sqrt{-x^2+3x+4}.f(x)=\sqrt{-x^2+3x+4}.

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