Annalise makes rectangular patchwork quilts out of leftover fabric scraps. The first scrap she is using to make a quilt has a wi
1 answer:
Answer:
Area =
Step-by-step explanation:
The function is the area function of a rectangle.
Area of Rectangle = Length * Width
Length of fabric scrap = 5x
Length of rectangular patchwork will be 5x + 3
and
Width of fabric scrap = 2x
Width of rectangular patchwork will be 2x + 5
THus, Area = (5x+3)(2x+5) square feet.
Let's expand:
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Answer:
(-5, 0) ∪ (5, ∞)
Step-by-step explanation:
I find a graph convenient for this purpose. (See below)
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When you want to find where a function is increasing or decreasing, you want to look at the sign of the derivative. Here, the derivative is ...
f'(x) = 4x^3 -100x = 4x(x^2 -25) = 4x(x +5)(x -5)
This has zeros at x=-5, x=0, and x=5. The sign of the derivative will be positive when 0 or 2 factors have negative signs. The signs change at the zeros. So, the intervals of f' having a positive sign are (-5, 0) and (5, ∞).
