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: If you are using a calculator, simply enter 64÷320×100 which will give you 20 as the answer.
Step-by-step explanation: Hope it helps:)
and tryna mark a child brainlest ;)
Hello...
Tony and his three friends live in Albuquerque, New Mexico, but they all attend college in Boston, Massachusetts. Because they want to have a car at school this year, they are planning to drive Tony's car from Albuquerque to Boston at the beginning of the school year. Although they'll each pay for their own food during the road trip, the friends plan to split the costs for gas and hotels evenly between the four of them.
Estimate the total cost that each friend will have to pay for gas and hotels. Explain how you got your answer. Here are some figures that may help you out:
•Tony's car can travel 28 miles for each gallon of gas.
•The average fuel cost at the time of their trip is $3 per gallon.
•They plan to drive about 650 miles each day.
•They estimate the average cost of a hotel each night is $85.
•They will drive approximately 2,240 miles to get from Albuquerque to Boston.
Solution:
Cost of Gas:
2240 / 28 x 3 = $240
Cost of Lodging:
85 x floor2240 / 650 = $255
Cost of both: $240 +255 = $495.
The cost for a 1/4 share is $495/4 = $123.75.
Answer:
Values that make it equal:
-4, -3, -1, 0, 4
Written equivalent inequality:
h≥−4
Step by Step for the written inequality:
h/4 ≥−1
Multiply both sides by 4. Since 4 is positive, the inequality direction remains the same.
h≥−4
I hope this helps you!! :)
