What does the derivative of a function represent geometrically?, The slope of the tangent line to the curve at a point., What does it mean if the derivative of a function is zero at a point?, The function has a horizontal tangent—possibly a maximum, minimum, or inflection point., What does the term "derivative" mean in calculus?, It describes how a quantity changes with respect to another—often how fast something is changing., What rule do you use when differentiating a function inside another function?, The chain rule., How do you find where a function reaches its maximum or minimum?, Set the first derivative equal to zero and analyze the critical points., What does it mean if the first derivative is positive?, The function is increasing at that point., What does it mean if the second derivative is negative?The graph is concave down, indicating a possible maximum., The graph is concave down, indicating a possible maximum., What does it mean when a function is increasing?, Its derivative is greater than zero., What does it mean when a function is concave up?, Its second derivative is greater than zero., How can you tell if a point is an inflection point?, The second derivative changes sign at that point.

Differentiation

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