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Mathematics
13.04.2023 19:58
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The slope at any point on the graph of the function h(x) where h(1)=9 is given by

The slope at any point on the graph of the function h(x) where h(1)=9 is given by the expression dy/dx=.

Write an expression for h(x) in terms of x.
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lex2678
lex2678
5,0(98 marks)

The given differential equation is separable:

\dfrac{\mathrm dy}{\mathrm dx} = 2x\sqrt y\implies\dfrac{\mathrm dy}{\sqrt y}=2x\,\mathrm dx

Integrate both sides:

2\sqrt y=x^2+C

In this case, y=h(x), so that given h(1)=9, we get

2\sqrt9=1^2+C\implies C=5

so that

2\sqrt{h(x)}=x^2+5\implies h(x)=\left(\dfrac{x^2+5}2\right)^2=\dfrac{x^4+10x^2+25}4

korar87181
korar87181
4,5(19 marks)
Correct answer to the question is letter b

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