#### To determine

**To find:**

We have to find the interval on which the function fx=e3x-ex is increasing.

#### Answer

The function is increasing on 12ln13,∞.

#### Explanation

**Calculation:**

We first take derivatives to find the increase or decrease of function.

As we know that if first derivative of function i.e. dfdx>0 then function is increasing.

So dfdx=3e3x-ex=ex3e2x-1

Since,ex>0. So, to show dfdx>0. We 3e2x-1 should be greater than zero.

Or 3e2x-1>0

Or

e2x>13

Or

x>12ln13

So, the interval on which f(x) is increasing is 12ln13,∞.

**Final statement:** The function is increasing on 12ln13,∞.