It should be the first option listed for Plan A and the last option listed for Plan B.
Answer:
- increasing: (π/2, 3π/2)
- decreasing: [0, π/2) ∪ (3π/2, 2π]
- minimum: -16 at x=π/2
- maximum: 16 at x=3π/2
Step-by-step explanation:
If all you want are answers to the questions, a graphing calculator can provide them quickly and easily. (see attached)
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If you need an algebraic solution, you need to find the zeros of the derivative.
f'(x) = -16cos(x)sin(x) -16cos(x) = -16cos(x)(sin(x) +1)
The product is zero where the factors are zero, at x=π/2 and x=3π/2.
These are the turning points, where the function changes from decreasing to increasing and vice versa.
(sin(x)+1) is non-negative everywhere, so the sign of the derivative is the opposite of the sign of the cosine function. This tells us the function f(x) is increasing on the interval (π/2, 3π/2), and decreasing elsewhere (except where the derivative is zero).
The function local extrema will be where the derivative is zero, so at f(π/2) (minimum) and f(3π/2) (maximum). We already know that cos(x) is zero there, so the extremes match those of -16sin(x).
Answer:
1/6
Step-by-step explanation:
the form you're using is slope-intercept. That is
y=mx+b
where y= y coordinate
m=slope
x= x coordinate
and b= y intercept
so, m in that equation is 1/6, so the slope is 1/6
Hope this helps!
Answer:
-35
Step-by-step explanation:
X's cancel out each other
-10+-25
There is a square and a half circle.
To find the radius of the circle: 18in - 12in = 6in
Area of a circle = (pi)r^2 = 3.14 (6in)^2 = 3.14 (36in^2) = 113.04in^2
This is an half circle, so we have to divide by 2 the result
56.52in^2 in what we’re looking for.
Area of the square = (12in)^2 = 144in^2
Total area = (144 + 56.52)in^2 = 200.52in^2
Or 201in^2 to the nearest whole number.