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GuDViN [60]
4 years ago
15

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

Mathematics
1 answer:
jonny [76]4 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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