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:
Ken is planting vegetables in his garden. He has 20 seeds. Determine whether 20 is prime or composite number. If it is composite, list all of the ways Ken can arrange the seeds in even rows.
Answer:
The answer is 8.3 repeating. If you round it the answer is 8.
Answer: 75%.
Step-by-step explanation: 3/4 as a percentage is 75%.