The mean weight of the packages is 2.5, so the total weight of the packages is found by multiplying 2.5 pounds by 4 which is equal to 10 pounds. That is the tial weight of the four books. To find the weight of the fourth book, the three other weights are subtracted from 10 pounds:
Answer:
1674.12
Step-by-step explanation:
I hope it helps.
Answer with Step-by-step explanation:
Given

Differentiating both sides by 'x' we get

Now we know that for an increasing function we have
![f'(x)>0\\\\14cos(2x)+7cos(x)>0\\\\2cos(2x)+cos(x)>0\\\\2(2cos^{2}(x)-1)+cos(x)>0\\\\4cos^{2}(x)+cos(x)-2>0\\\\(2cos(x)+\frac{1}{2})^2-2-\frac{1}{4}>0\\\\(2cos(x)+\frac{1}{2})^2>\frac{9}{4}\\\\2cos(x)>\frac{3}{2}-\frac{1}{2}\\\\\therefore cos(x)>\frac{1}{4}\\\\\therefore x=[0,cos^{-1}(1/4)]\cup [2\pi-cos^{-1}(1/4),2\pi ]](https://tex.z-dn.net/?f=f%27%28x%29%3E0%5C%5C%5C%5C14cos%282x%29%2B7cos%28x%29%3E0%5C%5C%5C%5C2cos%282x%29%2Bcos%28x%29%3E0%5C%5C%5C%5C2%282cos%5E%7B2%7D%28x%29-1%29%2Bcos%28x%29%3E0%5C%5C%5C%5C4cos%5E%7B2%7D%28x%29%2Bcos%28x%29-2%3E0%5C%5C%5C%5C%282cos%28x%29%2B%5Cfrac%7B1%7D%7B2%7D%29%5E2-2-%5Cfrac%7B1%7D%7B4%7D%3E0%5C%5C%5C%5C%282cos%28x%29%2B%5Cfrac%7B1%7D%7B2%7D%29%5E2%3E%5Cfrac%7B9%7D%7B4%7D%5C%5C%5C%5C2cos%28x%29%3E%5Cfrac%7B3%7D%7B2%7D-%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%5Ctherefore%20cos%28x%29%3E%5Cfrac%7B1%7D%7B4%7D%5C%5C%5C%5C%5Ctherefore%20x%3D%5B0%2Ccos%5E%7B-1%7D%281%2F4%29%5D%5Ccup%20%5B2%5Cpi-cos%5E%7B-1%7D%281%2F4%29%2C2%5Cpi%20%5D)
Similarly for decreasing function we have
![[tex]f'(x)](https://tex.z-dn.net/?f=%5Btex%5Df%27%28x%29%3C0%5C%5C%5C%5C%5Ctherefore%20cos%28x%29%3C1%2F4%5C%5C%5C%5Cx%3Ccos%5E%7B-1%7D%28%5Cfrac%7B1%7D%7B4%7D%29%5C%5C%5C%5Cx%3D%5Bcos%5E%7B-1%7D%28%5Cfrac%7B1%7D%7B4%7D%29%2C2%5Cpi%20-cos%5E%7B-1%7D%28%5Cfrac%7B1%7D%7B4%7D%29%5D)
Part b)
To find the extreme points we equate the derivative with 0

Thus point of extrema is only 1.
Answer:
rational
Step-by-step explanation: