Rui is a professional deep water free diver.
His altitude (in meters relative to sea level), xxx seconds after diving, is modeled by:
d(x)=\dfrac{1}{2}x^2 -10xd(x)=
2
1
x
2
−10xd, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 2, end fraction, x, start superscript, 2, end superscript, minus, 10, x
What is the lowest altitude Rui will reach?

the correct question is
Rui is a professional deep water free diver. His altitude (in meters relative to sea level), xxx seconds after diving, is modeled by: d(x)=1/2x^2 -10x What is the lowest altitude Rui will reach?

we have that
d(x)=(1/2)x² -10x

we know that
the function is quadratic (a parabola)
so
the lowest altitude (depth) is the vertex

using a graph tool
see the attached figure

the vertex is the point (10,-50)
that means
His altitude (in meters relative to sea level), 10 seconds after diving is 50 meters under the sea level

therefore
the answer is
the lowest altitude is 50 meters under the sea level

psm22415 psm22415 · Answer 2 · 2022-05-05T18:00:37+02:00

The lowest altitude is 50 meters under sea level.

What is the differentiation?

Differentiation is a process, in Maths, where we find the instantaneous rate of change in function based on one of its variables.

Rui is a professional deep-water-free diver.

His altitude (in meters relative to sea level), d(x) = (1/2)x² - 10x.

The lowest altitude Rui will reach is given by;

d(x) = (1/2)x² - 10x

d'(x) = x - 10

putting d'(x) = 0

x - 10 = 0

x = 10

d''(x) = 1

d(x) has minimum value when x = 10

d(x) = (1/2)x² - 10x

d(10) = (1/2)10² - 10(10)

= 50 - 100

= -50

Hence, the lowest altitude is 50 meters under sea level.

Learn more about differentiation;

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