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Sumi Vora

🎥**Watch: AP Calculus AB/BC - ****Concavity** & **f, f', f''**

If we look at the first derivative of a function, we can see that if the rate of change of the function is increasing on an interval, the function is **concave up**. Likewise, if the rate of change of the function is decreasing, the function is **concave down**.

We can determine whether the first derivative is increasing or decreasing by taking the derivative of the derivative (aka the **second derivative**). 🕵

If f"(a) = 0, then c is a special point called a **point of inflection**, which occurs when the function switches concavity. At a point of inflection, f(x) is neither concave up or concave down; it is linear at that point. 💡

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Unit 10: Infinite Sequences and Series (BC Only)

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Unit 1: Limits & Continuity

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Unit 2: Differentiation: Definition & Fundamental Properties

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Unit 3: Differentiation: Composite, Implicit & Inverse Functions

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Unit 4: Contextual Applications of the Differentiation

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Unit 5: Analytical Applications of Differentiation

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Unit 6: Integration and Accumulation of Change

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Unit 7: Differential Equations

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Unit 8: Applications of Integration

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Unit 9: Parametric Equations, Polar Coordinates & Vector Valued Functions (BC Only)