4.3

original equation

first derivative

Set equal to zero

Solve for x, and then plug numbers from in between

intervals into the equation.

- + + +

decreasing from to –6

increasing from –6 to

from the intervals of increase and decrease, we

know the minimum is at –6 because that is where it

goes from decreasing to increase

second derivative, set equal to zero and solve for x again

and plug in the numbers from in between the intervals back to

+ - +

concave up from to –4, and from 0 to

concave down from –4 to 0

4.3 Example:

Find the local max and min values of f using both the first derivative test.

F(x)=

U=x V=x+4

V’= 2X Use the quotient rule to find

Put and solve for the critical points

- + -

(-2)—(2) Put your critical points into a number line and see where it changes from positive to negative or negative to positive.