Answer:
(i) The derivative of the function is
.
(ii) The domain of all first order polynomials (linear functions) is the set of all real numbers. That is:
![Dom\{f(x)\} = \mathbb{R}](https://tex.z-dn.net/?f=Dom%5C%7Bf%28x%29%5C%7D%20%3D%20%5Cmathbb%7BR%7D)
The domain of all zero order polynomials (constant functions) is the set of all real numbers. That is:
![Dom\{f'\} = \mathbb{R}](https://tex.z-dn.net/?f=Dom%5C%7Bf%27%5C%7D%20%3D%20%5Cmathbb%7BR%7D)
Step-by-step explanation:
(i) <em>Find the derivative of the function using the definition of derivative</em>:
The derivative is defined by the following limit:
(1)
If we know that
, then the definition of derivative is expanded:
![f' = \lim_{h \to 0} \frac{\frac{1}{10}\cdot (x+h) - \frac{1}{3}-\frac{1}{10}\cdot x +\frac{1}{3}}{h}](https://tex.z-dn.net/?f=f%27%20%3D%20%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7B%5Cfrac%7B1%7D%7B10%7D%5Ccdot%20%28x%2Bh%29%20-%20%5Cfrac%7B1%7D%7B3%7D-%5Cfrac%7B1%7D%7B10%7D%5Ccdot%20x%20%2B%5Cfrac%7B1%7D%7B3%7D%7D%7Bh%7D)
![f' = \lim_{h \to 0} \frac{\frac{1}{10}\cdot h }{h}](https://tex.z-dn.net/?f=f%27%20%3D%20%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7B%5Cfrac%7B1%7D%7B10%7D%5Ccdot%20h%20%7D%7Bh%7D)
![f' = \lim_{h \to 0} \frac{1}{10}](https://tex.z-dn.net/?f=f%27%20%3D%20%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7B1%7D%7B10%7D)
![f' = \frac{1}{10}](https://tex.z-dn.net/?f=f%27%20%3D%20%5Cfrac%7B1%7D%7B10%7D)
The derivative of the function is
.
(ii) <em>State the domain of the function and the domain of its derivative</em>:
The domain of all first order polynomials (linear functions) is the set of all real numbers. That is:
![Dom\{f(x)\} = \mathbb{R}](https://tex.z-dn.net/?f=Dom%5C%7Bf%28x%29%5C%7D%20%3D%20%5Cmathbb%7BR%7D)
The domain of all zero order polynomials (constant functions) is the set of all real numbers. That is:
![Dom\{f'\} = \mathbb{R}](https://tex.z-dn.net/?f=Dom%5C%7Bf%27%5C%7D%20%3D%20%5Cmathbb%7BR%7D)
Answer:
what do u want to find I don't get it
Answer:
65.4 degrees
Step-by-step explanation:
cos(x) = 5/12
x = arccos(5/12), which is approximately 65.3756816 (on calculator). to the nearest tenth that is 65.4
Answer:
Mizuki here to answer!
The correct answer would be 15 inches!
Step-by-step explanation:
7200 ÷ (24 x 20) = 15
Answer:
91
Step-by-step explanation: