Calculus Exam

[Sniffer]

I need help with the following questions, can anybody help?

Find the height h of the elliptical contour x^2 - xy + 2y^2 = 7

The volume of a sphere of radius x is V = (4/3)piex^3. The radius is increasing at a constant rate of 2 units per second and has value 3 units when the time is zero. Determine the rate of change of the volume at time five.


The equation x^3 - x + = 0 has only one solution and it lies in the interval [-2, 0]. Find it.

Thanks for your help Sniffer

 

[Unco]

G'day, Sniffer.

For the first one:
I solved for y using the quadratic formula and plotted. It is a tilted ellipse and I'm not sure what we are supposed to take the "height" to be.

The second one is a reasonably standard rate of change question:
\(\displaystyle \frac{dV}{dt} = \frac{dV}{dx} \times \frac{dx}{dt}\)
which part are your stuck on?

The third one is incomplete! It could be that we need to use numerical methods (eg. Newton-Raphson); the cubic formula or . . . .