Self-Test 04 - Differentiation

Check your understanding

This self-test lets you check your understanding of Session 04. It is purely formative: nothing is tracked or graded, and nobody sees your answers. Work through the Tasks first, then use this quiz to confirm the ideas have stuck. A wrong answer triggers a 10-second cooldown before you can retry, so think before you click.

1. Geometrically, the derivative \(f'(a)\) is:

2. Which rule differentiates \((3x + 1)^5\)?

3. Let \(f(x) = x^3\). Compute \(f'(2)\). Type the number.

4. What is \(\dfrac{d}{dx}\,e^x\)?

5. Let \(f(x) = x^2 + 4x\). Compute \(f'(3)\). Type the number.

Rules of Differentiation

6. What is \(\dfrac{d}{dx}\,\ln x\)?

7. The product rule says \((f \cdot g)'\) equals:

8. Let \(f(x) = \dfrac{x+3}{x+1}\). Compute \(f'(0)\). Type the number.

Tangents & Curvature

9. If \(f''(x) \geq 0\) on an interval, the graph there is:

10. Let \(f(x) = x^2 - 4x + 1\). What is the slope of the tangent line at \(x = 5\)? Type the number.

Marginal Analysis

11. The marginal cost \(C'(q)\) is measured in:

12. The elasticity of demand is \(\varepsilon = -0.5\). Demand is … and a small price increase …

Well done. You solved every question. You can apply the power, product, quotient and chain rules, differentiate \(e^x\) and \(\ln x\), find tangent slopes, read curvature from \(f''\), and interpret marginal cost and elasticity. You are ready for Session 05 on optimization.