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: 5.76
Step-by-step explanation:
0.09 x 64 implies 0.09 in 64 places
To solve this, Multiply 0.09 x 64
It gives 5.76
2* 100 + 2 * 65 = 330 perimeter
100 * 65 = 6,500 area
2*90 + 2*75 = 330 perimeter
90 * 75 = 6,750 area
Answer: There would be 12,000 bacteria 8 hours after the initial infection.
Step-by-step explanation: You start with 25 cells and if they divide every 15 minutes, 25 multiplied by 15 gets you 375 cells every quarter of an hour. Then if you multiply that by the 32 quarter hours, you get 12,000 cells. To check that you can also multiply 25 by 15, still 375, then 375 by 4 for each quarter of the hour, then that gets you 1,500 cells every hour. If you multiply that by 8 for the 8 hours they have time to divide, you still get 12,000 cells.
I hope this helps!
