How to Find f(x) from f''(x) | Full Step-by-Step Integration with Conditions (Easy Explanation!)

In this step-by-step calculus tutorial, we solve a common exam-style question:

You're given the second derivative:
➡️ f''(x) = 18x + 8
And two initial conditions:
➡️ f'(2) = 46
➡️ f(0) = 8

We’ll use integration to recover the original function \( f(x) \).

🎯 This video is perfect for:
KCSE Form 4 students studying calculus
First-year university or college students learning basic integration
Anyone who wants to improve their understanding of how to move from a second derivative back to the original function

📚 What you’ll learn:
✅ How to integrate a second derivative step-by-step
✅ How to apply initial conditions to find constants
✅ How to write the final function f(x) accurately

📌 This method is essential in both high school and college-level calculus exams.

🎓 Whether you’re in Kenya studying for KCSE 2025 or in university tackling early calculus, this whiteboard walkthrough makes it clear and simple.

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