Section 3.1 Higher Order Derivatives, Velocity and Acceleration
The second derivative is the derivative of the derivative, that is
f'(f'(x))= f”(x)
If the position of an object is s(t) with respect to time, then
the velocity is v(t)=s'(t)=\(\frac{ds}{dt}\)
Velocity can be v(t)>0 or v(t)<0
And the acceleration is
a= \(\frac{dv}{dt}\) = \(\frac{d²s}{dt²}\)
Acceleration can be \(\frac{d²s}{dt²}\) >0 (accelerating) or \(\frac{d²s}{dt²}\) <0 (decelerating)
Speed is the magnitude of the velocity, speed = |v(t)|= |s'(t)|
Section 3.2 Maximum or Minimum on an interval (Extreme values)
Algorithm : If a function f(x) is continuous and differentiable on the interval I = p ≤ x ≤q
Calculate f'(x) at every point on the interval I, wher f'(x)=0 and the end-points x= p and x=q. The maximum value is where f(x) has the largest value and the minimum value is where f(x) has the smallest value.
Section 3.3 Optimization problems
In an optimization problem, determine the maximum and the minimum on the interval.
This can be applied to profit, cost and revenue in terms of units produced in the manufacturing process.
Economic situations always involve minimizing costs or maximizing profits.
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