Question

f:R—>R, f(x)=8-5x,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)=8-5x

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

f : R----->R , f(x) = 8 - 5x

we know, any function, f(x) is increasing in (a,b) only when f'(x) > 0 in interval (a, b) while decreasing only when f'(x) < 0 in interval (a,b) .

f(x) = 8 - 5x

differentiate with respect to x,

f'(x) = -5 < 0 for all x belongs to R

here, we see, f(x) is decreasing in all real value of x.