Matematika - LS 24/25

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Vyřešte nerovnici

6x^2+30x-41\geq -5.

\langle1, \infty)

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\langle-5, \infty)

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\langle-6,1\rangle

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\langle-6, \infty)

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(-\infty, \infty)

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(-\infty,-6\rangle\cup\langle1, \infty)

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Spočtěte derivaci dané funkce

f(x)=x\cdot\frac{5x-2}{2x-7}.

\frac{30x^2-78x+14}{(2x-7)^2}

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Žádná z předchozích odpovědí není správně.

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\frac{-70x+14}{(2x-7)^2}

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\frac{10x-2}{2}

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\frac{10x^2-70x+14}{(2x-7)^2}

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Určete definiční obor funkce

f(x)=\textrm{arcsin}(\frac{x}{6}-9).

\langle53, 55\rangle

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(54,\infty)

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\langle-1, 1\rangle

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(-\infty, 6)\cup (6,\infty)

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\langle48, 60\rangle

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Spočtěte hodnotu f ' (2), když f(x)=x^3+2x^2-4x+4

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Určete definiční obor funkce

f(x)=\log(\frac{-2x+2}{4-2x})+\log(5).

(1, 2)

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\langle1, 2)

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(-\infty,1)\cup(2,\infty)

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(-\infty, 1)

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(-\infty,1\rangle\cup(2,\infty)

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(-\infty, 2)

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Vyřešte nerovnici

\frac{-3x-3}{6x-6}\leq -1.

(1,\infty)

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(-\infty,-1\rangle\cup(1,\infty)

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(1, 3\rangle

✅

\langle -1,1)

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(-\infty,1)\cup\langle3, \infty)

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(-\infty, 1)

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Nalezněte definiční obor funkce dané předpisem f(x)=\sqrt{-x^2-5x+14}.

\mathcal{D}_f=\emptyset

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Žádná z odpovědí a–d není správně.

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\mathcal{D}_f=(-\infty,-7\rangle\cup\langle2,\infty)

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\mathcal{D}_f=(-\infty,-4\rangle\cup\langle4,\infty)

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\mathcal{D}_f=\mathbf{R}

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Vyřešte nerovnici

-4x^2-4x-4\geq1.

(-\infty,-2)

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(-\infty,\infty)

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(-2,6)

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(-\infty,64)

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(-64,64)

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\emptyset

✅

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