will be increasing on the intervals where
and decreasing wherever
. Local extrema occur when
and the sign of
changes to either side of that point.
is positive when
is between -4 and some number between -2 and -1, and also 2 (exclusive) and 4, so you can estimate that
is increasing on the intervals [-4, -2] and (2, 4].
is negative when
is between some number between -2 and -1, up to some number less than 2. So
is decreasing on the interval [-1, 1].
You then have two possible cases for extrema occurring. The sign of
changes for some
between -2 and -1, and again to either side of
.
Answer: 6 inches
Step-by-step explanation:
The diameter is double the radius
Undefined
Slope is equal to the change in
y
y
over the change in
x
x
, or rise over run.
The change in
x
x
is equal to the difference in x-coordinates (also called run), and the change in
y
y
is equal to the difference in y-coordinates (also called rise).
Substitute in the values of
x
x
and
y
y
into the equation to find the slope.
The expression contains a division by
0
0
The expression is undefined.
A "rational expression" is a fraction in which the numerator and the denominator are both polynomials. The sum of two such expressions will always produce another such expression, viz.,
<span>p(x)/q(x) + r(x)/s(x) = [p(x)s(x) + q(x)r(x)] / [q(x)*s(x)]. </span>
<span>The numerator and denominator of the sum will both be polynomials when fully expanded</span>
