Finding Values

[Guest]

Problem 1
What is the value of c between 3 and 5 for y= x + 3/x? The mean value theorem must be used.

This what I have thus far;
(1-3/c^2) = [(5+3/5)-(3+3/3)]/[5-3], where do I go from here?


Problem 2
If the initial condition curve y contains the point (0,4), what is the value of the constant of intergration if you take the antiderivative of dy/dx?



Problem 3

What is the value of the constant of integration if you take the specific antiderivative of dy/dx = X^3 + 2X, with an initial condition of (1,2)


Help please!

 

[skeeter]

Problem 1
What is the value of c between 3 and 5 for y= x + 3/x? The mean value theorem must be used.

This what I have thus far;
(1-3/c^2) = [(5+3/5)-(3+3/3)]/[5-3], where do I go from here?

what else? solve for c ...
1 - 3/c^2 = [(28/5) - 4]/2
1 - 3/c^2 = 4/5
1/5 = 3/c^2
c^2 = 15
now ... which root of the above equation is the one guaranteed by the MVT?

Problem 2
If the initial condition curve y contains the point (0,4), what is the value of the constant of intergration if you take the antiderivative of dy/dx?

something missing here? it depends on the function.
for instance ...
suppose dy/dx = 2x
y = x^2 + C
since y(0) = 4 ...
4 = 0 + C, and C = 4
however ...
suppose dy/dx = -sin(x)
y = cos(x) + C
4 = cos(0) + C
C = 3 in this case


Problem 3

What is the value of the constant of integration if you take the specific antiderivative of dy/dx = X^3 + 2X, with an initial condition of (1,2)

antiderivative is y = (x^4)/4 + x^2 + C
substitute your values given by the initial condition and solve for C ...
2 = (1^4)/4 + 1^2 + C


Help please!

 

[Guest]

Value Reply Thanks

Thanks for your help!
Once you explain it , I said wow! I see it!