I believe the answer is c there is no x value as there is no solution
It looks like the limit you want to compute is
![\displaystyle \lim_{x\to4} \frac{f(g(x)) - f(4)}{x-4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%5Cto4%7D%20%5Cfrac%7Bf%28g%28x%29%29%20-%20f%284%29%7D%7Bx-4%7D)
Since
, this limit corresponds exactly to the derivative of
at
. Recall that
![f'(a) = \displaystyle \lim_{x\to a} \frac{f(x) - f(a)}{x - a}](https://tex.z-dn.net/?f=f%27%28a%29%20%3D%20%5Cdisplaystyle%20%5Clim_%7Bx%5Cto%20a%7D%20%5Cfrac%7Bf%28x%29%20-%20f%28a%29%7D%7Bx%20-%20a%7D)
By the chain rule,
![(f\circ g)'(4) = f'(g(4)) \times g'(4) = f'(4) \times g'(4) = 3\times7 = \boxed{21}](https://tex.z-dn.net/?f=%28f%5Ccirc%20g%29%27%284%29%20%3D%20f%27%28g%284%29%29%20%5Ctimes%20g%27%284%29%20%3D%20f%27%284%29%20%5Ctimes%20g%27%284%29%20%3D%203%5Ctimes7%20%3D%20%5Cboxed%7B21%7D)
Since
exists,
is differentiable at
so it must be continuous.
The correct place for it in the .04
Answer:
hobbies and going to the movies
if you can only choose one go with movies
Step-by-step explanation:
Questions:
A clothing manufacturer uses the model a = √(f + 4) - √(36 - f) to estimate the amount of fabric to order from a mill. In the formula, a is the number of apparel items (in hundreds) and f is the number of units of fabric needed. If 400 apparel items will be manufactured , how many units of fabric should be ordered?
Answer:
32 units of fabrics
Step-by-step explanation:
Given
![a = \sqrt{f + 4} - \sqrt{36 - f}](https://tex.z-dn.net/?f=a%20%3D%20%5Csqrt%7Bf%20%2B%204%7D%20-%20%5Csqrt%7B36%20-%20f%7D)
Required
Find f when a = 4
Substitute 4 for a
![4 = \sqrt{f + 4} - \sqrt{36 - f}](https://tex.z-dn.net/?f=4%20%3D%20%5Csqrt%7Bf%20%2B%204%7D%20-%20%5Csqrt%7B36%20-%20f%7D)
Rewrite as:
![\sqrt{36 - f} + 4 = \sqrt{f + 4}](https://tex.z-dn.net/?f=%5Csqrt%7B36%20-%20f%7D%20%2B%204%20%3D%20%5Csqrt%7Bf%20%2B%204%7D)
Square both sides
![(\sqrt{36 - f} + 4)^2 = (\sqrt{f + 4})^2](https://tex.z-dn.net/?f=%28%5Csqrt%7B36%20-%20f%7D%20%2B%204%29%5E2%20%3D%20%28%5Csqrt%7Bf%20%2B%204%7D%29%5E2)
![(\sqrt{36 - f} + 4)^2 = f + 4](https://tex.z-dn.net/?f=%28%5Csqrt%7B36%20-%20f%7D%20%2B%204%29%5E2%20%3D%20f%20%2B%204)
![36 - f + 8\sqrt{36 - f} + 16 = f + 4](https://tex.z-dn.net/?f=36%20-%20f%20%2B%208%5Csqrt%7B36%20-%20f%7D%20%2B%2016%20%3D%20f%20%2B%204)
Collect Like Terms
![8\sqrt{36 - f}= f +f+ 4 - 36 -16](https://tex.z-dn.net/?f=8%5Csqrt%7B36%20-%20f%7D%3D%20f%20%2Bf%2B%204%20-%2036%20-16)
![8\sqrt{36 - f}= 2f -48](https://tex.z-dn.net/?f=8%5Csqrt%7B36%20-%20f%7D%3D%202f%20-48)
Divide through by 2
![4\sqrt{36 - f}= f -24](https://tex.z-dn.net/?f=4%5Csqrt%7B36%20-%20f%7D%3D%20f%20-24)
Square both sides
![16(36-f) = (f - 24)^2](https://tex.z-dn.net/?f=16%2836-f%29%20%3D%20%28f%20-%2024%29%5E2)
![16(36-f) = f^2 - 48f + 576](https://tex.z-dn.net/?f=16%2836-f%29%20%3D%20f%5E2%20-%2048f%20%2B%20576)
![576-16f = f^2 - 48f + 576](https://tex.z-dn.net/?f=576-16f%20%3D%20f%5E2%20-%2048f%20%2B%20576)
![-16f = f^2 - 48f](https://tex.z-dn.net/?f=-16f%20%3D%20f%5E2%20-%2048f)
Collect like terms
![f^2 - 48f + 16f = 0](https://tex.z-dn.net/?f=f%5E2%20-%2048f%20%2B%2016f%20%3D%200)
![f^2 -32f = 0](https://tex.z-dn.net/?f=f%5E2%20-32f%20%3D%200)
Factorize
![f(f - 32) = 0](https://tex.z-dn.net/?f=f%28f%20-%2032%29%20%3D%200)
or ![f = 32](https://tex.z-dn.net/?f=f%20%3D%2032)
f can not be 0 because some units must be ordered.
So, f = 32