Given:
![f(x)=\sqrt[]{5x^2-2}](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%5B%5D%7B5x%5E2-2%7D)
f(X) will be differentiated by chain rule.
![\begin{gathered} f^{\prime}(x)=\frac{1}{2\sqrt[]{5x^2-2}}\lbrack5(2x)\rbrack \\ f^{\prime}(x)=\frac{5x}{\sqrt[]{5x^2-2}} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20f%5E%7B%5Cprime%7D%28x%29%3D%5Cfrac%7B1%7D%7B2%5Csqrt%5B%5D%7B5x%5E2-2%7D%7D%5Clbrack5%282x%29%5Crbrack%20%5C%5C%20f%5E%7B%5Cprime%7D%28x%29%3D%5Cfrac%7B5x%7D%7B%5Csqrt%5B%5D%7B5x%5E2-2%7D%7D%20%5Cend%7Bgathered%7D)
The correct answer is y = 1/8x^2
Number of weekend minutes used: x
Number of weekday minutes used: y
This month Nick was billed for 643 minutes:
(1) x+y=643
The charge for these minutes was $35.44
Telephone company charges $0.04 per minute for weekend calls (x)
and $0.08 per minute for calls made on weekdays (y)
(2) 0.04x+0.08y=35.44
We have a system of 2 equations and 2 unkowns:
(1) x+y=643
(2) 0.04x+0.08y=35.44
Using the method of substitution
Isolating x from the first equation:
(1) x+y-y=643-y
(3) x=643-y
Replacing x by 643-y in the second equation
(2) 0.04x+0.08y=35.44
0.04(643-y)+0.08y=35.44
25.72-0.04y+0.08y=35.44
0.04y+25.72=35.44
Solving for y:
0.04y+25.72-25.72=35.44-25.72
0.04y=9.72
Dividing both sides of the equation by 0.04:
0.04y/0.04=9.72/0.04
y=243
Replacing y by 243 in the equation (3)
(3) x=643-y
x=643-243
x=400
Answers:
The number of weekends minutes used was 400
The number of weekdays minutes used was 243
