Holiday Reflection

Review blog again:
Section 5.4
To solve for a variable when it’s an exponent:
1. Take the ln of both sides.
2. Bring the variable to the front of the ln.
To solve for a variable if it’s inside a log:
1. Rewrite as an exponent.
2. Solve for x.

EXAMPLES
1) 6 = e^x-2
ln6 = lne^x-2
ln6 = x-2
x = ln6-2

2) ln(3x-2) = 9
e^9 = 3x-2
e^9+2 = 3x
x = e^9+2/3

3) e^x = 12
lne^x = ln12
x = ln12
~ 2.485

Finding a max or min is the same thing as finding a horizontal tangent line.
STEPS:
1. Take derivative, and set equal to 0.
2. Find any place the function is not
differentiable.
3. Plug in to get y-value if asking about max or
min specifically.
4. If on an interval plug in to get a y-value.
5. Highest > max
Lowest > min

Example:
1) f(x) = t/t-2 (3,5)
1. f'(x)= -2 = 0
x = 0
2. aymptote at 2
3. h'(0)= 0
4. h(3) = 3
h(5) = 5/3
5. max > 3
min > 0