So given these two functions:
f(x) = e^(-2x + 3)
g(x) = √(ax)
how can you find the value of a, given that the two curves intersect perpendicularly??
the way i see it is that you have to many unknowns (i equated the derivatives).
Help much appreciated!!! thanks!!!
The solution to the intersection point can only be found numerically so it is next to impossible to find an expression for a that way. However we can be tricky.Originally Posted by Yehia
First we are looking for a point x such that f(x) = g(x). That is we have a point x = b on the functions f(x) and g(x) such that
Now, perpendicular slopes follow the rule that m' = -1/m. So we are looking for a at the intersection point such that
Evaluate this at x = b and see if you can use the intersection condition to write this equation as a function of a only.
-Dan
Dan, I did EXACTLY that. i ended up with BOTH those equations, BUT both happened to be the same. can you please show me the way forward or at least do it yourself and see if you get an answer?The solution to the intersection point can only be found numerically so it is next to impossible to find an expression for a that way. However we can be tricky.
First we are looking for a point x such that f(x) = g(x). That is we have a point x = b on the functions f(x) and g(x) such that
Now, perpendicular slopes follow the rule that m' = -1/m. So we are looking for a at the intersection point such that
Evaluate this at x = b and see if you can use the intersection condition to write this equation as a function of a only.
-Dan
Ok, i went on and now i end up with:
At the intersection point we have f(b) = g(b), or
Also we know that g'(b) = -1/f'(b), so
But what does the intersection point equation say thatis equal to?
-Dan
b^5 = e^(12-8b)
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