Verify if the function is increasing y = 3x^3 + 3^x .

Given the function y=3x^3 + 3^x.

We
need to determine whether y is an increasing
function.

To verify, we need to determine the first derivative (
y').

If y' is positive, then the function is
increasing.

If y' is negative, then the function is
decreasing.

Now, let us determine the first
derivative:

y= 3x^3 + 3^x

==> y'
= ( 3x^3)' + (3^x) '

            = 9x^2 + (3^x)* ln
3

Now let us analyze y'.

We know that
x^2 is always positive.

Then, 9x^2 also
positive.

Also, 3^x is always
positive.

Then, (3^x)* ln3 is
positive.

Then, we conclude that y' is
positive.

Then, the function y is an increasing
function for all R numbers.