B.
Step-by-step explanation:
2 ways to solve this: using calculus or not using calculus
not using calculus: we know |x| + b will move graph up by b amount of units, but since there is no b, the minimum f(x) value is f(x) = 0
finding x now
0 = |5x+1|
since 0 is neither positive nor negative, we can remove absolute value signs without creating 2 equations
0 = 5x + 1
- 1 = 5x
x =
using calculus (disregard if you are not in calculus)
setting f(x) = y
finding critical points, where is 0 or undefined
is undefined at x =
testing left and right sides of our critical points to see if it is a max or min point
use easy values for this
at x = 0, = 5
at x = -1, = -5
since goes from negative to positive at x = ,
x = is a relative minimum
since x = is our only critical point, it is also our absolute minimum (relative minimums do not always correspond to absolute minimums)