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GuDViN [60]
3 years ago
15

Find f. f'(x)=(sqrt(x))(6+10x) f(1)=11

Mathematics
1 answer:
jonny [76]3 years ago
3 0
It is a matter of integrating <span>f′</span><span>:

</span>f(x)=\int \sqrt{x}(6+10x)dx,&#10;\\&#10;\\f(x)=\int 6x^{1/2}dx+\int10x^{3/2}dx,&#10;\\&#10;\\f(x)=4x^{3/2}(x+1)+C.&#10;

Combine the constants. Then use the initial condition to find C<span>:
</span>
11=8+C\implies C=3

Therefore,

f(x)=4x^{3/2}(x+1)+3.
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When f(x) = 2x 2 + 3, find f(-3).<br> -15<br> 21<br> 39
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Answer:

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Step-by-step explanation:

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6 0
3 years ago
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The 3rd and 4th choices are appropriate.

_____
This is what is known as a "logistic function." It is used to model population growth when there is a resource limit. It starts out exponential, but then slows as it reaches the "carrying capacity" of the environment. The lower asymptote is zero; the upper one is the carrying capacity of the resource--here 15/1 = 15.

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