Consider the function below. (If an answer does not exist, enter DNE.) g(x) = 190 + 8x3 + x4 (a) Find the interval of increase. (Enter your answer using interval notation.)

The interval of increase of g(x) is .

Step-by-step explanation:

The interval of increase occurs when first derivative of given function brings positive values. Let be , the first derivative of the function is:

The following condition must be met to define the interval of increase:

The first term is always position due to the quadratic form, the second one is a first order polynomial and it is known that positive value is a product of two positive or negative values. Then, the second form must satisfy this:

The solution to this inequation is:

Now, the solution to this expression in interval notation is:

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

read more on -

step-by-step explanation: