Application of Derivatives

Question 1

LInearization

Answer 1

Approximating where you will be after a certain change in time or whatever the x value is.

F(x+deltax)=f(x)+deltaxf’(x)
X(t+deltat)=x(t)+deltatx’(t)

Question 2

Newton method

Answer 2

Used linearization to find roots.

X1=xo-yo/f’(xo)

F’(xo)=yo/(xo-x1)

Question 3

Optimization and Differentiation steps

Answer 3

1. Visualize it
2. Define it
3. Write an equation
4. Find the min/max (derivative end points)
5. Answer the question