Application of the Second Derivative (Acceleration)
Key Questions

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 060 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 060 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

Relationship between First and Second Derivatives of a Function

Analyzing Concavity of a Function

Notation for the Second Derivative

Determining Points of Inflection for a Function

First Derivative Test vs Second Derivative Test for Local Extrema

The special case of x⁴

Critical Points of Inflection

Application of the Second Derivative (Acceleration)

Examples of Curve Sketching