Answer:
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To solve this, you have to know that the first derivative of a function is its slope. When an interval is increasing, it has a positive slope. Thus, we are trying to solve for when the first derivative of a function is positive/negative.
f(x)=2x^3+6x^2-18x+2
f'(x)=6x^2+12x-18
f'(x)=6(x^2+2x-3)
f'(x)=6(x+3)(x-1)
So the zeroes of f'(x) are at x=1, x=-3
Because there is no multiplicity, when the function passes a zero, he y value is changing signs.
Since f'(0)=-18, intervals -3<x<1 is decreasing(because -3<0<1)
Thus, every other portion of the graph is increasing.
Therefore, you get:
Increasing: (negative infinite, -3), (1, infinite)
Decreasing:(-3,1)
Answer:
11 dimes, 17 nickels
Step-by-step explanation:
d + n = 28, put one variable by itself on a side, d = 28 - n
.10d + .05n = 1.95
Sub the first equation into the second
.10(28 - n) + .05n = 1.95
2.8 - .10n + .05n = 1.95
2.8 - .05n = 1.95
-.05n = -0.85
n = 17 nickels
d + 17 = 28
d = 11 11 dimes
She cuts off 21 cm. this leaves 63cm. cut into 6 equal pieces gives 10.5 cm pcs
