Answer:
the function is decreasing on the interval (-∞,-2) and increasing on the interval (-2,∞)
B
Step-by-step explanation:
first we take the first derivative
x²+4x-1 = 2x+4
set this equal to 0 and solve
2x+4= 0
2x= -4
x= -2
we then have two intervals
(-∞,-2) u (-2,∞)
to find out whether something is decreasing on increasing on these intervals just plug in any number in the interval
if the result is positive it's increasing
if it's negative it's decreasing
Let's plug in x= -4 for the interval (-∞, -2)
2(-4)+4= -4
it's negative so it's decreasing on this interval
let's then plug in x=0 for the interval (-2,∞)
2(0)+4= 4
this is positive so it's increasing on this interval
So the function is decreasing on the interval (-∞,-2) and increasing on the interval (-2,∞)
which is equal to to B
