Final Review – Calculus Basics

Congratulations! You have completed the full beginner calculus course.

Here is a quick recap of the main concepts:

Limits: foundation of calculus (approaching values)
Continuity & IVT: no jumps, takes all intermediate values
Derivatives: instantaneous rate of change, slope of tangent
Basic rules: power, constant, sum/difference
Product, quotient, chain rules: for composite functions
Higher derivatives: concavity, acceleration, jerk
Implicit differentiation: when y not isolated
Related rates: connected changing quantities
Optimization: max/min using critical points
Curve sketching: using first/second derivatives
Antiderivatives & integrals: reverse of derivatives, area under curve

Now let’s test everything together!

Exercise 1

Exercise 2

Match the concept to its meaning/application (drag to first empty zone):

Derivative → Drop here
Second derivative → Drop here
Integral → Drop here
Chain rule → Drop here

Click / tap any item to place it in the first empty zone:

Instantaneous rate of change / slope

Concavity / acceleration

Accumulated change / area under curve

Differentiate composite functions

Exercise 3

Which statements are true? (Select all that apply)

\(f'(x) = 0\) at critical points (possible max/min) \(f''(x) > 0\) means concave up (local min if critical point) \(\int f(x) dx\) gives family of antiderivatives \(+ C\) Related rates problems require implicit differentiation All continuous functions are differentiable Chain rule is used in gradient descent backpropagation

Final Advice & Next Steps

You now understand:

Limits as foundation
Derivatives: rates, slopes, optimization
Integrals: accumulation, area

Practice daily — try small Python/NumPy visualizations of derivatives/integrals.

Next steps:

Definite integrals & Fundamental Theorem applications
Area between curves, volumes
Gradient descent intuition (ML)
Books: "Calculus" by Stewart, "Calculus Made Easy" by Silvanus P. Thompson

Thank you for completing the course! You are ready for more advanced topics.

Keep learning — you’ve got this!

Lesson 16: Final Review & Comprehensive Practice

Final Review – Calculus Basics

Exercise 1

Exercise 2

Exercise 3

Final Advice & Next Steps