#### To determine

**To find:**

We have to find the interval on which the curve is concave downward.

#### Answer

The interval on which the curve is concave downward is 0,14ln92.

#### Explanation

**Calculation:**

To determine concavity we calculate the second derivative of the function.

The equation of the curve is

y=2ex-e-3x

Then differentiate two times with respect to *x,* we have

d2yd2x=2ex-9e-3x

This curve is concave downward if d2yd2x<0.

So, to find the interval on which curve is concave downward. We have to find the value of *x* for which d2yd2x<0.

2ex-9e-3x<0

Or

2ex<9e-3x

Or

2e4x<9

Or

e4x<92

Taking natural logarithmic on both sides, we have

4x<ln92

Or

x<14ln92

So, the interval on which the curve y=2ex-e-3x is concave downward is -∞,14ln92.

**Conclusion:**

The interval on which the curve is concave downward is 0,14ln92.