Application of the Second Derivative (Acceleration)
Key Questions
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Let us first find the velocity function
#v(t)# .
#v(t)=s'(t)=3t^2+6t# Let us now find the acceleration function
#a(t)# .
#a(t)=v'(t)=s''(t)=6t+6# -
Answer:
Acceleration is change in velocity over time
#A=V/T# Explanation:
For example lets say you have a car and its 0-60 MPH time is 3 seconds so the equation is
#A=60/3# so you would take 60 and divide it by three and that is 20 so the 0-60 speed is 20 seconds. -
Answer:
Take the second derivative.
Explanation:
If you have a position function
#x(t)# , then the derivative is a velocity function#v(t) = x'(t)# and the second derivative is an acceleration function#a(t) = x''(t)# .
Questions
Graphing with the Second Derivative
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Relationship between First and Second Derivatives of a Function
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Analyzing Concavity of a Function
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Notation for the Second Derivative
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Determining Points of Inflection for a Function
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First Derivative Test vs Second Derivative Test for Local Extrema
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The special case of x⁴
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Critical Points of Inflection
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Application of the Second Derivative (Acceleration)
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Examples of Curve Sketching