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A particle moves along the curve below. y = 8 + x3 As it reaches the point (1, 3), the y-coordinate is increasing at a rate of 3 cm/s. How fast is the x-coordinate of the point changing at that instant?

Respuesta :

Answer:

Change of rate of x coordinate=1 cm/s

Step-by-step explanation:

Given that

[tex]y=8+x^3[/tex]

Now differentiate with respect to time in both side

So [tex]\dfrac{dy}{dt}=0+3 x^2\dfrac{dx}{dt}[/tex]

Given  that y-coordinate is increasing at a rate of 3 cm/s

So [tex]\dfrac{dy}{dt}=3[/tex]

Also given that coordinates (1,3)

So x=1

Now by putting the values

[tex]3=0+3\times 1^2\dfrac{dx}{dt}[/tex]

So  [tex]\dfrac{dx}{dt}=1[/tex]

Change of rate of x coordinate=1 cm/s

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