Question

f:R—>R, f(x)=3x+7,Determine the intervals in which F is increasing and the intervals in which F is decresing.

Answer 1

Dear student:

Given:F:R—>R

f(x)=3x+7,

For determining the intervals in which F is increasing and decreasing.

Find derivative of f(x)

then see the derivative in which f is positive and negative.

If it is positive then f is increasing

And if it is negative then f is decreasing.

See the attachment.

Answer 2

Dear student,

Answer: given function f is increasing in R

Solution: steps of solution are as follows

1) differentiate the given function with respect to X

2) check whether f'(x) is greater than zero or less than zero

3) if it is greater than zero then function is increasing otherwise decreasing

$f: \: f(x) = 3x + 7 \\ \\ f'(x) = 3 \\ \\ f'(x) > 0$
as that you can see that f'(x) is free from x, for any value of x, it always remains greater than zero,thus the given function is increasing in the entire range of real numbers

Function is increasing in R.

Hope it helps you.