This preview shows page 1. Sign up to view the full content.
Unformatted text preview: y = ln (3 + x ) concave up? d2y SOLUTION: POWER RULE: EXAMPLE:
SOLUTION: properties of logarithms.
Step 3. Differentiate both sides with respect to x y ′ = sec 2 sec e sin ( x ) ⋅ sec e sin ( x ) tan e sin ( x ) ⋅ (( www.prep101.com dy
+ 2y ⋅
(x + 2 y ) = −2 x − y
2x + y .
x + 2y LOGARITHMIC DIFFERENTIATION:
to differentiate a function with complicated
exponent/a product of several functions, etc. It’s
also used to differentiate functions that have an x
in both the base and in the exponent. f(x) is concave down on that interval. A point of
inflection occurs when f ( p ) changes sign (and
Vertical asymptote: The line x = a is a vertical
asymptote for the graph of the function f(x) if
and only if lim f ( x ) = ±∞ or
x→a + lim f ( x) = ±∞ . x→a − Horizontal asymptote: The line x = b is a
horizontal asymptote for the graph of the
function f(x) if and only if lim f ( x) = b or...
View Full Document