Is the function f(x) = −2x + 5 increasing or decreasing? Explain how you know.

Answer 1

In the given function f(x) =-2x+5 its a linear expression . firstly derivate the expression we get -2 so its less than 0 in any intervals so it is always a decreasing function

Answer 2

The calculus approach is to take the first derivative which is -2. Therefore the function is decreasing

because the derivative is ALWAYS negative

for x in (a,b), b > a --> b -a > 0 ---> a-b < 0

Then

, f(b) - f(a) = (-2b+5) - (-2a+5)

= -2b + 5 + 2a - 5

= -2b + 2a

= 2a - 2b

= 2(a-b) < 0 , per the above

So then f(b) - f(a) < 0 --> f(b) < f(a) for all x in (a,b)

which is a DECREASING function