If f(x) = x², then the function is increasing for?
A
x > 0
B
x < 0
C
All x
D
None
Analysis & Theory
f'(x) = 2x. For x > 0, derivative > 0 ⇒ function increasing.
If f(x) = -x², then the function is decreasing for?
A
x > 0
B
x < 0
C
All x
D
None
Analysis & Theory
f'(x) = -2x. For x > 0, derivative < 0 ⇒ function decreasing.
If f(x) = eˣ, then the function is?
A
Always increasing
B
Always decreasing
C
Constant
D
Increasing only for x > 0
Analysis & Theory
f'(x) = eˣ > 0 for all x ⇒ function is always increasing.
If f(x) = ln(x), then the function is?
A
Always increasing for x > 0
B
Always decreasing for x > 0
C
Constant
D
None
Analysis & Theory
f'(x) = 1/x > 0 for x > 0 ⇒ ln(x) is increasing for x > 0.
If f(x) = cos(x), then the function is decreasing in?
A
(0, π)
B
(π, 2π)
C
(-π/2, π/2)
D
All x
Analysis & Theory
f'(x) = -sin(x). On (0, π), sin(x) > 0 ⇒ derivative < 0 ⇒ decreasing.
If f(x) = sin(x), then the function is increasing in?
A
(0, π)
B
(-π/2, π/2)
C
(π, 2π)
D
All x
Analysis & Theory
f'(x) = cos(x). On (-π/2, π/2), cos(x) > 0 ⇒ sin(x) increasing.