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Matematika - LS 24/25

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Určete maximální intervaly konvexity a konkávnosti funkce

f:y=-x^3+12x^2-36x-8f:y=-x^3+12x^2-36x-8.
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Určete maximální intervaly monotonie funkce

f:y=e^x(-2x-8)f:y=e^x(-2x-8).
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Nalezněte asymptoty grafu y= \frac{2x^2}{16x^2-1}y= \frac{2x^2}{16x^2-1}.
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Jaká musí být hodnota čísla q, aby přímka 2x+2y+q=0 byla normálou grafu y=-3x²+7x+8?
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Spočtěte limitu \displaystyle\lim_{x\to-\infty} \frac{3x^2+8x+2}{4x^2+1x+2}\displaystyle\lim_{x\to-\infty} \frac{3x^2+8x+2}{4x^2+1x+2}

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Spočtěte limitu

\displaystyle\lim_{x\to -6}\frac{x^2+11x+30}{x^2+13x+42}\displaystyle\lim_{x\to -6}\frac{x^2+11x+30}{x^2+13x+42}
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Spočtěte absolutní minimum (nejmenší funkční hodnotu) funkce f(x)=2x^3+8x^2+3f(x)=2x^3+8x^2+3 pro x\in\langle -8,8\ranglex\in\langle -8,8\rangle.

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Jaká musí být hodnota čísla q, aby přímka 16x-4y+q=0 byla tečnou grafu y=-4x²-4x+5?
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Určete maximální intervaly konvexity a konkávnosti funkce

f:y=-x^3-9x^2-24x-5f:y=-x^3-9x^2-24x-5.
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Určete maximální intervaly monotonie funkce

f:y=e^x(9x+9)f:y=e^x(9x+9).
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