The critical values of the function are x = 0 and x = 64
The critical values of a function f(x) are the values of x for which f'(x) = 0.
Given,
f(x) = ![\frac{x^{4} }{5(x-8)^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7B4%7D%20%7D%7B5%28x-8%29%5E%7B2%7D%20%7D)
The derivative is found as follows, applying the quotient rule:
f'(x) = ![\frac{[5(x^{4} )(x-8)^{2}-5x^{4} [(x-8)^{2} ]' }{[5(x-8)^{2} ]^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7B%5B5%28x%5E%7B4%7D%20%29%28x-8%29%5E%7B2%7D-5x%5E%7B4%7D%20%5B%28x-8%29%5E%7B2%7D%20%5D%27%20%7D%7B%5B5%28x-8%29%5E%7B2%7D%20%5D%5E%7B2%7D%20%20%7D)
= ![\frac{2x^{3}(x-64) }{5(x-8)^{3} }](https://tex.z-dn.net/?f=%5Cfrac%7B2x%5E%7B3%7D%28x-64%29%20%7D%7B5%28x-8%29%5E%7B3%7D%20%7D)
The zeros of the function are the zeros of the numerator, thus:
![2x^{3} (x-64) =0\\2x^{3} =0-------- > x =0\\](https://tex.z-dn.net/?f=2x%5E%7B3%7D%20%28x-64%29%20%3D0%5C%5C2x%5E%7B3%7D%20%3D0--------%20%3E%20x%20%3D0%5C%5C)
x - 64 = 0------------->x = 64
The critical values are x = 0 and x = 64
Learn more about critical values here:brainly.com/question/12958088
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Answer:
7minutes
Step-by-step explanation:
so if 48 books are sorted in 120 seconds what about 168 books if you cross multiply you will get 420 seconds which converted to minutes is 7
Answer: x=8
Step-by-step explanation:
Since we are given that ∠ABC and ∠DBC are complementary angles, we know that adding them together should give us 90°. We can use this to solve for x.
6x+13+4x-3=90 [combine like terms]
10x+10=90 [subtract both sides by 10]
10x=80 [divide both sides by 10]
x=8
Now, we know that x=8.
<span>Only –3 is an extraneous solution.
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