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).
<h2>Greetings!</h2>
Answer:
w² + 5w = Area
Step-by-step explanation:
The equation for an area of a rectangle is:
Length x Width = area
If w is the width, and length is 5 units longer than the width, then length can be classed as w + 5
Simply multiply these two values to find the area:
w + (w + 5) =
(w * w) + (w * 5)
w² + 5w = area
This is the area formula as no area has been given, nor can this be simplified.
<h2>Hope this helps!</h2>
-3x+5y=10 (add 3x on both side)
5y=3x+10 ( divide 5 to each term)
y=3/5x+2
slope is 3/5
y-intercept is 2
2/3 of a box per 30 secs
2/3 times 2 = 4/3 = 1 1/3