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Aleks [24]
4 years ago
10

E=300-10 (30) How to solve it step by step

Mathematics
1 answer:
Zepler [3.9K]4 years ago
6 0

Answer:

Step-by-step explanation:

e = 300-10(30)

e = 300 - 300

e = 0

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Use calculus to find the absolute maximum and minimum values of the function. (round all answers to three decimal places.) f(x)
Allisa [31]
Part A:

Given the function f(x)=x+2\cos(x), the absolute maximum or minimum occurs when f'(x)=0.

f'(x)=0 \\  \\ \Rightarrow1-2\sin{x}=0 \\  \\ \Rightarrow2\sin{x}=1 \\  \\ \Rightarrow\sin{x}= \frac{1}{2}  \\  \\ \Rightarrow x=\sin^{-1}{\frac{1}{2}}= \frac{\pi}{6}

Using the second derivative test,

f''(x)=-2cosx \\  \\ \Rightarrow f''\left( \frac{\pi}{6} \right)=-2\cos{\left( \frac{\pi}{6} \right)}=-1.732

Since the second derivative gives a negative number, the given function has a maximum point at x=\frac{\pi}{6}.

And the maximum point is given by:

f\left( \frac{\pi}{6} \right)=\frac{\pi}{6}+2\cos\left( \frac{\pi}{6} \right) \\  \\ =0.5236+2(0.8660)=0.5236+1.732 \\  \\ =\bold{2.256}

i.e. \left(\frac{\pi}{6},\ 2.256\right)



Part B:

Given the function f(x)=e^{-x}-e^{-2x}, the absolute maximum or minimum occurs when f'(x)=0.

f'(x)=0 \\ \\ \Rightarrow-e^{-x}+2e^{-2x}=0 \\ \\ \Rightarrow2e^{-2x}=e^{-x} \\ \\ \Rightarrow2e^{-x}=1 \\ \\ \Rightarrow e^{-x}=\frac{1}{2} \\  \\ \Rightarrow-x=\ln \frac{1}{2}=-0.6931 \\  \\ \Rightarrow x=0.6931

Using the second derivative test,

f''(x)=e^{-x}-4e^{-2x} \\ \\ \Rightarrow f''(0.6931)=e^{-0.6931}-4e^{-2(0.6931)} \\  \\ =0.5-4e^{-1.386}=0.5-4(0.25)=0.5-1 \\  \\ =-0.5

Since the second derivative gives a negative number, the given function has a maximum point at x=0.6931.

And the maximum point is given by:

f(0.6931)=e^{-0.6931}-e^{-2(0.6931)} \\  \\ =0.5-e^{-1.386}=0.5-0.25=\bold{0.25}

i.e. (0.693, 0.25)
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2 and 3 because 2 is in 6 timestable and 3 is in 9 as the lowest number
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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Part A: A graph passes through the points (0, 2), (2,6), and (3. 12). Does this graph represent a linear
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Answer:

The function given is non-linear.

Step-by-step explanation:

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Hope this helps.

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