2015 AP Calculus 2c  AP Calculus AB solved exams  AP Calculus AB  Khan Academy  Summary and Q&A
TL;DR
Calculate the rate at which a function changes by finding the derivative using a calculator.
Key Insights
 ❓ The task involves finding the derivative of a function using a calculator.
 🚦 The provided function h(x) represents the vertical distance between two other functions.
 ❓ Using a calculator is especially useful for tasks involving derivatives and integrals.
 ☠️ The calculated rate of change is approximately 3.812 when x=1.8.
 ❓ The analysis highlights the importance of conceptual understanding alongside calculator usage.
 ⁉️ The question emphasizes the conceptual application of derivatives and integrals in problemsolving scenarios.
 😒 The use of a calculator with derivative capabilities saves time and aids in quickly evaluating the desired rate of change.
Transcript
 [Voiceover] Let h be the vertical distance between the graphs of f and g and region s. Find the rate at which h changes with respect to x when x is equal to 1.8. We have region s right over here. You can't see it that well since I drew over it. And what you see when we're in region s, the function f is greater than the function g. It's above the ... Read More
Questions & Answers
Q: What is the main objective of this analysis?
The main objective is to determine the rate of change of the vertical distance between two functions when x=1.8.
Q: How is the function h(x) defined?
The function h(x) is defined as the difference between f(x) and g(x), where f(x) is 1+x+e^(x^22x) and g(x) is x^4.
Q: What tool can be used to calculate the derivative of a function?
A calculator with derivative capabilities can be used to numerically evaluate the derivative of a function.
Q: Why is it important to understand the underlying conceptual ideas of derivatives and integrals?
Understanding the underlying concepts of derivatives and integrals helps in solving problems and utilizing calculators effectively.
Summary & Key Takeaways

The task is to find the rate of change of the vertical distance between two functions (h) with respect to x when x=1.8.

By subtracting one function (g) from another function (f), h(x) is defined.

The derivative of h(x) can be calculated using a calculator, and when x=1.8, the rate of change is approximately 3.812.