Answer:
- The instantaneous rate of increase of f(x) at
is 3. - One possible equation of this line is y = 3x - 16.
- The line is tangent to the graph of y = f(x). The slope of the line is the same as the instantaneous rate of increase of f(x) at .
Step-by-step explanation:
<h3>1.</h3>
![\begin{aligned}&\lim_{h\to 0}{\frac{f(3+h)-f(h)}{h}}\\ =&\lim_{h\to 0}\frac{1}{h} \cdot [(3^{3} + 3 \times 3^{2}h +3\times 3h^{2} + h^{3})- 4(3^{2} + 2\times 3h + h^{2}) + 2 \\[-1em] &\phantom{\lim_{h\to 0}\frac{1}{h}\cdot []} -(3^{3} -4\times 3^{2} + 2)]\\ = &\lim_{h \to 0}\frac{h^{3} + 5h^{2} +3h}{h}\\=& \lim_{h \to 0}{h^{2}} + \lim_{h \to 0}{5h} + \lim_{h\to 0}{3}\\ =& 3\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%26%5Clim_%7Bh%5Cto%200%7D%7B%5Cfrac%7Bf%283%2Bh%29-f%28h%29%7D%7Bh%7D%7D%5C%5C%20%3D%26%5Clim_%7Bh%5Cto%200%7D%5Cfrac%7B1%7D%7Bh%7D%20%5Ccdot%20%5B%283%5E%7B3%7D%20%2B%203%20%5Ctimes%203%5E%7B2%7Dh%20%2B3%5Ctimes%203h%5E%7B2%7D%20%2B%20h%5E%7B3%7D%29-%204%283%5E%7B2%7D%20%2B%202%5Ctimes%203h%20%2B%20h%5E%7B2%7D%29%20%2B%202%20%5C%5C%5B-1em%5D%20%26%5Cphantom%7B%5Clim_%7Bh%5Cto%200%7D%5Cfrac%7B1%7D%7Bh%7D%5Ccdot%20%5B%5D%7D%20-%283%5E%7B3%7D%20-4%5Ctimes%203%5E%7B2%7D%20%2B%202%29%5D%5C%5C%20%3D%20%26%5Clim_%7Bh%20%5Cto%200%7D%5Cfrac%7Bh%5E%7B3%7D%20%2B%205h%5E%7B2%7D%20%2B3h%7D%7Bh%7D%5C%5C%3D%26%20%5Clim_%7Bh%20%5Cto%200%7D%7Bh%5E%7B2%7D%7D%20%2B%20%5Clim_%7Bh%20%5Cto%200%7D%7B5h%7D%20%2B%20%5Clim_%7Bh%5Cto%200%7D%7B3%7D%5C%5C%20%3D%26%203%5Cend%7Baligned%7D)
.
<h3>2.</h3>
.
In other words, the graph of y = f(x) passes through the point (3, -7) where 
.
The point-slope form of a line in a cartesian plane is:
.
For this line,
is the point on the line, while
is the slope of the line.
The equation of this line will thus be
.
That's equivalent to
.
<h3>3.</h3>
Refer to the diagram attached. The line touches the graph of y = f(x) at x = 3 without crossing it. The line here is thus a tangent to the graph of y = f(x) at x = 3. The slope of the line represents the instantaneous rate of increase of f(x) at .
Answer:
11 6/9
Step-by-step explanation:
Daniel works in a market
He has large bags of potatoes that weighs 26 1/4
Daniel is going to sell them in smaller bags 9/4 pounds each
Therefore the number of smaller bags of potatoes in which Daniel would have filled can be calculated as follows
= 26 1/4 ÷ 9/4
= 105/4 ÷ 9/4
= 105/4 × 4/9
= 105/9
= 11 6/9
Answer:
1
Step-by-step explanation:
To find the slope, you must subtract the second y axis from the first y axis then the second x axis from the first x axis.
Problem: (5, 3) (-2, -4)
Solution: Step 1. - 4 - 3 = 7 (subtract the second y axis from the first y axis)
Step 2. - 2 - 5 = 7 (subtract the second x axis from the first x axis)
Answer: 7/7
Final Answer: 1
Mark me as brainliest!!
6x - 4 < 8
Add 4 to both sides:
6x < 12
Divide both sides by 6:
x < 2
Answer: x < 2
Answer:
It's 81
Step-by-step explanation:
2^5 is 2*2*2*2*2 or 32
7^2 is 7*7 or 49
Add them together... 81
