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Matematika - LS 24/25

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Určete definiční obor funkce

f(x)=\textrm{arccos}(\frac{x}{4}+8).f(x)=\textrm{arccos}(\frac{x}{4}+8).
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Určete definiční obor funkce

f(x)=\log(\frac{2x+6}{5-5x})+\log(9).f(x)=\log(\frac{2x+6}{5-5x})+\log(9).
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Vyřešte nerovnici

\frac{-2x-4}{3x-6}< -1.\frac{-2x-4}{3x-6}< -1.
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Vyřešte nerovnici

-5x^2+4x+2\leq6.-5x^2+4x+2\leq6.
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Vypočtěte nejmenší reálné číslo, které je řešením soustavy nerovnic

10 ≤ 3 - 7x ≤ 20. Zaokrouhlete na dvě desetinná místa.

 

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Spočtěte derivaci dané funkce

f(x)=x\cdot e^{4x}\cdot(5x+8).f(x)=x\cdot e^{4x}\cdot(5x+8).
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Spočtěte f ' (-4), když f(x)=(8x²-7)/(x-5).

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Spočtěte hodnotu f ' (1), když f(x)=x^3+2x^2-5x+6f(x)=x^3+2x^2-5x+6
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Na vhodném intervalu zderivujte funkci f(x)=\frac{x^3}{3}-\sqrt{6}.f(x)=\frac{x^3}{3}-\sqrt{6}.
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Určete definiční obor funkce

f(x)=\textrm{arccos}(\frac{x}{8}-4).f(x)=\textrm{arccos}(\frac{x}{8}-4).
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