Consider the curve defined by x^2=e^x-y for x>0. At what value of x does the curve have a horizontal tangent?​

For , the curve have a horizontal tangent.

Explanation:

Let for . By Differential Calculus we know that a curve of the form if and only if . Since the expression defined above is an implicit function, we need to apply implicit differentiation and clear the symbol for the first derivative, that is:

(1)

If we know that , then the value of so that the curve have a horizontal tangent is:

For , the curve have a horizontal tangent.