What is the maximum value of the function y=1-2 sin x?

Mathematics

1 answer:

Pepsi [2]3 years ago

8 0

Answer:

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Step-by-step explanation:

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The curve with equation y=e^2x/4+3e^x has one stationary point.find the exact value of the coordinates of this point

Softa [21]

$y=\dfrac{e^{2x}}{4+3e^x}$
$\implies y'=\dfrac{2e^{2x}(4+3e^x)-3e^xe^{2x}}{(4+3e^x)^2}$
$\implies y'=\dfrac{8e^{2x}+3e^{3x}}{(4+3e^x)^2}$

Stationary points occur where the derivative is zero. The denominator is positive for all $x$ , so we only need to worry about the numerator.

$8e^{2x}+3e^{3x}=e^{2x}(8+3e^x)=0$

$e^{2x}>0$ for all $x$ , so we can divide through:

$8+3e^x=0\implies e^x=-\dfrac83$

But $e^x>0$ for all $x\in\mathbb R$ , so this function has no stationary points...

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3 years ago

Solve the system using elimination. Write the solution as an ordered pair. (1 point) SHOW YOUR WORK FOR FULL CREDIT! (2 points)

Gre4nikov [31]

Answer: (1,-1)

Step-by-step explanation:

- You can multiply the first equation by -1

- Add the equations.

- Solve for x, as following:

$\left \{ {{-5x - 4y = -1} \atop {-3x + 4y = -7}} \right.\\------\\-8x=-8\\x=1$