For the curve represented by the equation below, find the point of inflection(s).

First, find the second derivative of $$f(x)$$ .
Hint 2
Set $$f''(x)=0$$ to solve for the inflection point.
An inflection point is a point on the curve/graph at which concavity changes, and occurs when $$f''(x)=0$$ .
Using the power rule for the first derivative and applying it twice, we’ll get the second derivative power rule:
Thus, the second derivative is:
Note that $$\frac{d(e^u)}{dx}=e^u\frac{du}{dx}$$ , which is why $$e^x$$ remains unchanged after performing the second derivative. Solving for $$x$$ when $$f''(x)=0$$ to get the x-component inflection point:
The inflection point consists of both a $$x$$ and $$y$$ coordinate. We have solved the $$x$$ component, but still need to determine the $$y$$ component. To find $$y$$ , plug the $$x$$ component back into the original function:
Thus, the inflection point is at (1.39, 0.15)
(1.39, 0.15)