On What Intervals Is the Function $f ( x ) = a x - b e ^ { x }$

question 152

Essay

On what intervals is the function $f ( x ) = a x - b e ^ { x }$ :
a)increasing?
b)decreasing?
c)concave up?
d)concave down?

---

Definitions:

Automatization

The process by which a task becomes automatic after extensive practice, requiring less cognitive effort to perform.

Practice Phase

A period in the learning process dedicated to repeated performance or exercise of a task, aiming to improve efficiency, accuracy, or understanding.

Cell Phone Use

The utilization of mobile phones for various purposes, including communication, entertainment, and accessing information.

Driving Errors

Mistakes made by drivers while operating a vehicle, which can range from perceptual errors to judgment lapses.