We will see that f'(x) > 0, which means that f(x) is an increasing function.
<h3>
How to prove that the function is increasing?</h3>
For any function f(x), if f'(x) > 0, then f(x) is increasing for any value of x.
Here we have the cubic function:
f(x) = x³ + 4x
If we differentiate this, we get:
f'(x) = df(x)/dx = 3x² + 4.
And notice that x² is always positive, then f'(x) > 0, which means that f(x) is an increasing function.
If you want to learn more about cubic functions:
brainly.com/question/20896994
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Answer:
65°
Step-by-step explanation:
The sum of the angles of a triangle is always 180°. Meaning, ∠P + ∠Q + ∠R = 180.
(2x-9) + (2x+4) + x = 180
Combine like terms:
5x-5 = 180
5x = 185
x = 37
P = (2x - 9) = 2(37) - 9 = 74 - 9 = 65
Answer:
Step-by-step explanation:
This is an exponential equation of the form

Answer:
b = 6 units
Step-by-step explanation:
Area = 1/2bh
8 = 1/2(b)(8/3)
divide both sides by 1/2
16 = b(8/3)
multiply both sides by 3
48 = 8b
divide both sides by 8
b = 6 units
For your boxes:
1/2 x b/1 x 8/3 = 8/1
b/1 x 8/3 = 16/1
8b/3 / 8 = 2/1
b/3 x 3 = 6
Answer:
CE = 17
Step-by-step explanation:
∵ m∠D = 90
∵ DK ⊥ CE
∴ m∠KDE = m∠KCD⇒Complement angles to angle CDK
In the two Δ KDE and KCD:
∵ m∠KDE = m∠KCD
∵ m∠DKE = m∠CKD
∵ DK is a common side
∴ Δ KDE is similar to ΔKCD
∴ 
∵ DE : CD = 5 : 3
∴ 
∴ KD = 5/3 KC
∵ KE = KC + 8
∵ 
∴ 
∴ 
∴ 
∴ 
∴ KC = (8 × 9) ÷ 16 = 4.5
∴ KE = 8 + 4.5 = 12.5
∴ CE = 12.5 + 4.5 = 17