Answer:
![f(216) \approx 6.0093](https://tex.z-dn.net/?f=f%28216%29%20%5Capprox%206.0093)
Step-by-step explanation:
Given
![\sqrt[3]{217}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B217%7D)
Required
Solve
Linear approximated as:
![f(x + \triangle x) \approx f(x) +\triangle x \cdot f'(x)](https://tex.z-dn.net/?f=f%28x%20%2B%20%5Ctriangle%20x%29%20%5Capprox%20f%28x%29%20%2B%5Ctriangle%20x%20%5Ccdot%20f%27%28x%29)
Take:
![x = 216; \triangle x= 1](https://tex.z-dn.net/?f=x%20%3D%20216%3B%20%5Ctriangle%20x%3D%201)
So:
![f(x) = \sqrt[3]{x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%7D)
Substitute 216 for x
![f(x) = \sqrt[3]{216}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%5B3%5D%7B216%7D)
![f(x) = 6](https://tex.z-dn.net/?f=f%28x%29%20%3D%206)
So, we have:
![f(x + \triangle x) \approx f(x) +\triangle x \cdot f'(x)](https://tex.z-dn.net/?f=f%28x%20%2B%20%5Ctriangle%20x%29%20%5Capprox%20f%28x%29%20%2B%5Ctriangle%20x%20%5Ccdot%20f%27%28x%29)
![f(215 + 1) \approx 6 +1 \cdot f'(x)](https://tex.z-dn.net/?f=f%28215%20%2B%201%29%20%5Capprox%206%20%20%2B1%20%5Ccdot%20f%27%28x%29)
![f(216) \approx 6 +1 \cdot f'(x)](https://tex.z-dn.net/?f=f%28216%29%20%5Capprox%206%20%20%2B1%20%5Ccdot%20f%27%28x%29)
To calculate f'(x);
We have:
![f(x) = \sqrt[3]{x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%7D)
Rewrite as:
![f(x) = x^\frac{1}{3}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E%5Cfrac%7B1%7D%7B3%7D)
Differentiate
![f'(x) = \frac{1}{3}x^{\frac{1}{3} - 1}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7B1%7D%7B3%7Dx%5E%7B%5Cfrac%7B1%7D%7B3%7D%20-%201%7D)
Split
![f'(x) = \frac{1}{3} \cdot \frac{x^\frac{1}{3}}{x}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Ccdot%20%5Cfrac%7Bx%5E%5Cfrac%7B1%7D%7B3%7D%7D%7Bx%7D)
![f'(x) = \frac{x^\frac{1}{3}}{3x}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7Bx%5E%5Cfrac%7B1%7D%7B3%7D%7D%7B3x%7D)
Substitute 216 for x
![f'(216) = \frac{216^\frac{1}{3}}{3*216}](https://tex.z-dn.net/?f=f%27%28216%29%20%3D%20%5Cfrac%7B216%5E%5Cfrac%7B1%7D%7B3%7D%7D%7B3%2A216%7D)
![f'(216) = \frac{6}{648}](https://tex.z-dn.net/?f=f%27%28216%29%20%3D%20%5Cfrac%7B6%7D%7B648%7D)
![f'(216) = \frac{3}{324}](https://tex.z-dn.net/?f=f%27%28216%29%20%3D%20%5Cfrac%7B3%7D%7B324%7D)
So:
![f(216) \approx 6 +1 \cdot f'(x)](https://tex.z-dn.net/?f=f%28216%29%20%5Capprox%206%20%20%2B1%20%5Ccdot%20f%27%28x%29)
![f(216) \approx 6 +1 \cdot \frac{3}{324}](https://tex.z-dn.net/?f=f%28216%29%20%5Capprox%206%20%20%2B1%20%5Ccdot%20%5Cfrac%7B3%7D%7B324%7D)
![f(216) \approx 6 + \frac{3}{324}](https://tex.z-dn.net/?f=f%28216%29%20%5Capprox%206%20%20%2B%20%5Cfrac%7B3%7D%7B324%7D)
![f(216) \approx 6 + 0.0093](https://tex.z-dn.net/?f=f%28216%29%20%5Capprox%206%20%20%2B%200.0093)
![f(216) \approx 6.0093](https://tex.z-dn.net/?f=f%28216%29%20%5Capprox%206.0093)
Answer:
Ummmm what’s the question?
Step-by-step explanation:
I will edit after you tell me what your question is.
Btw God bless you.have a great day!
Answer:
Step-by-step explanation:
Polynomial f(x) has the following conditions: zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.
The first part zeros of -4 means (x+4) and multiplicity 3 means (x+4)^3.
The second part zeros of 1 means (x-1) and multiplicity 1 means (x-1).
The third part f(0) = 320 means substituting x=0 into (x+4)^3*(x-1)*k =320
(0+4)^3*(0-1)*k = 320
-64k = 320
k = -5
Combining all three conditions, f(x)
= -5(x+4)^3*(x-1)
= -5(x^3 + 3*4*x^2 + 3*4*4*x + 4^3)(x-1)
= -5(x^4 + 12x^3 + 48x^2 + 64x - x^3 - 12x^2 - 48x - 64)
= -5(x^4 + 11x^3 + 36x^2 + 16x -64)
= -5x^3 -55x^3 - 180x^2 - 80x + 320
The total paycheck for the week is of $672 as Chris bacon work for 44 hours last week, regular pay $14 per hour and double time pay for overtime.
As given,
Regular pay per hour = $14
Overtime work payment= 2 × ($14)
Total hours work done last week = 44hours
Let regular timing be 8 hours per day 5 days a week
Total regular working hours = 8 × 5
= 40 hours
Over time = 44-40
= 4 hours
Payment check = (40 × 14)+ (4 × 28)
= $672
Therefore, The total paycheck for the week is of $672 as Chris bacon work for 44 hours last week.
Learn more about work here
brainly.com/question/18094932
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Step-by-step explanation: