If the first derivative of a function equals zero when x=c, what do we know? Pick the right answer. No explanation is required.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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If the first derivative of a function equals zero when x=c, what do we know? Pick the right answer. No explanation is required.

### Calculus Concepts: Identifying Critical Points

This section explores scenarios in which critical points occur in calculus, focusing on local maxima, minima, and tangent lines.

a) A local maximum exists when \( x = c \).

b) A local minimum exists when \( x = c \).

c) Either a or b.

d) A horizontal tangent line exists at \( x = c \).

e) Frogs are Purple.

Note: Options (a) through (d) relate to calculus and critical points, while option (e) is unrelated to this context. Consider this when evaluating the mathematical options above.
Transcribed Image Text:### Calculus Concepts: Identifying Critical Points This section explores scenarios in which critical points occur in calculus, focusing on local maxima, minima, and tangent lines. a) A local maximum exists when \( x = c \). b) A local minimum exists when \( x = c \). c) Either a or b. d) A horizontal tangent line exists at \( x = c \). e) Frogs are Purple. Note: Options (a) through (d) relate to calculus and critical points, while option (e) is unrelated to this context. Consider this when evaluating the mathematical options above.
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