Chapter 2: Q. 57 (page 185)
Use the definition of the derivative to find the derivatives described in Exercises 55-58.
Givenfindand
Short Answer
The value is
Chapter 2: Q. 57 (page 185)
Use the definition of the derivative to find the derivatives described in Exercises 55-58.
Givenfindand
The value is
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Get started for freeFor each function graphed in Exercises 65-68, determine the values of at which fails to be continuous and/or differentiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.
Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.
The line tangent to the graph of at the point
Stuart left his house at noon and walked north on Pine Street for minutes. At that point he realized he was late for an appointment at the dentist, whose office was located south of Stuart’s house on Pine Street; fearing he would be late, Stuart sprinted south on Pine Street, past his house, and on to the dentist’s office. When he got there, he found the office closed for lunch; he was minutes early for his appointment. Stuart waited at the office for minutes and then found out that his appointment was actually for the next day, so he walked back to his house. Sketch a graph that describes Stuart’s position over time. Then sketch a graph that describes Stuart’s velocity over time.
Velocity is the derivative of position . It is also true that acceleration (the rate of change of velocity) is the derivative of velocity. If a race car’s position in miles t hours after the start of a race is given by the function , what are the units of ? What are the units and real-world interpretation of ? What are the units and real-world interpretations of ?
Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.
The tangent line to at
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