Question

What is the maximum value of the derivative of f(x)= 3x^2+x^3

Answer 1

Answer:

Maximum Value: ∞

General Formulas and Concepts:

Calculus

Basic Power Rule:

• f(x) = cxⁿ
• f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

f(x) = 3x² + x³

Step 2: Find Derivative

1. Basic Power Rule:                    f'(x) = 2 · 3x²⁻¹ + 3 · x³⁻¹
2. Simplify:                                    f'(x) = 6x + 3x²

Step 3: Analyze

We see that our derivative is the graph of some sort of parabola. The parabola would be opening upwards.

Therefore, the maximum value of the derivative would be ∞, as the parabola's output y infinitely increases.