Download If they do not, then you must compute the area of each trapezoid

Problem of the Day Calculatorfunction such that g(x) < 0 for
If g is a differentiable
2
all real numbers x and if f '(x) = (x - 4) g(x), which
of the following is true?
A) f has a relative max at x = -2 and a relative min at x
=2
B) f has a relative min at x = -2 and a relative max at x
=2
C) f has relative minima at x = -2 and x = 2
D) f has relative maxima at x = -2 and x = 2
E) It cannot be determined if f has any relative extrema
Problem of the Day Calculatorfunction such that g(x) < 0 for
If g is a differentiable
2
all real numbers x and if f '(x) = (x - 4) g(x), which
of the following is true?
A) f has a relative max at x = -2 and a relative min at x
=2
B) f has a relative min at x = -2 and a relative max at x
=2
C) f has relative minima at x = -2 and x = 2
2
D) f has
relative
maxima
at x = to
-2 and
f '(x) = -(x - 4); graph
find x = 2
E) It cannot
be determined if f has any relative extrema
answer
Some functions do not have antiderivaties that are
elementary functions
∫sin x
2
Therefore the Fundamental Theorem of
Calculus cannot be applied
One approximation method for the area under a
curve is the Trapezoidal Rule
Instead of using rectangles as in lower and upper
sums or their limits, we use trapezoids
If the trapezoids have the same base length, you
can derive the following formula. (If they do not,
then you must compute the area of each
trapezoid separately.)
Trapezoidal Rule
derivation of this formula is
on page 309
Example
n=8
Example
n=8
≈1.974
The approximation is closer as the
number of subintervals increases
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