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A soap bubble stays spherical while its radius grows at… | StemPy Lab
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A soap bubble stays spherical while its radius grows at 0.5 mm/s. How fast is its volume growing at the moment when the radius is 4 mm?
Mathematics
Medium
High School (11–12)
Functions and Calculus › Application of Derivatives
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A soap bubble stays spherical while its radius grows at
0.5
mm/s
0.5\ \text{mm/s}
0.5
mm/s
. How fast is its volume growing at the moment when the radius is
4
mm
4\ \text{mm}
4
mm
?
201.1
mm
3
/
s
201.1\ \text{mm}^3/\text{s}
201.1
mm
3
/
s
100.5
mm
3
/
s
100.5\ \text{mm}^3/\text{s}
100.5
mm
3
/
s
50.3
mm
3
/
s
50.3\ \text{mm}^3/\text{s}
50.3
mm
3
/
s
25.1
mm
3
/
s
25.1\ \text{mm}^3/\text{s}
25.1
mm
3
/
s
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The function f(x) = x/(x² + 1) has derivative f'(x) = (1 - x²)/((x² + 1)²). On which interval is f strictly increasing? →
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