Help with solving graph equation (use of implicit differentiation)

• Dec 7th 2012, 09:10 PM
Help with solving graph equation (use of implicit differentiation)
Equation of graph : 2x5 + 2y2= 5xy
The vertical tangent line and the horizontal tangent line to the curve intersect at the point A(a,b). Find the coordinates of A.
The graph is shown on my paper. Maybe you guys can use an online graphing app to see how it looks like or use scientific calculator.
• Dec 7th 2012, 10:09 PM
MarkFL
Re: Help with solving graph equation (use of implicit differentiation)
When you implicitly differentiate with respect to $x$, what do you get for $\frac{dy}{dx}$ ?
• Dec 7th 2012, 10:25 PM
Re: Help with solving graph equation (use of implicit differentiation)
• Dec 7th 2012, 10:42 PM
MarkFL
Re: Help with solving graph equation (use of implicit differentiation)
Yes, good work! I would write this as:

$\frac{dy}{dx}=\frac{5(y-2x^4)}{4y-5x}$

Now, equating the numerator to zero will tell us where the curve has a horizontal tangent, white equating the denominator to zero will tell us where the vertical tangent occurs. What do you find?
• Dec 7th 2012, 10:56 PM