The second statement is the what of the first?
1 answer:
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<h3>Answer: y = x+1</h3>
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Explanation:
f(x) = x^3 - 2x + 3
f ' (x) = 3x^2 - 2 ..... apply the power rule
f ' (1) = 3(1)^2 - 2 ... plug in x coordinate of given point
f ' (1) = 1
If x = 1 is plugged into the derivative function, then we get the output 1. This means the slope of the tangent line at (1,2) is m = 1. It's just a coincidence that the x input value is the same as the slope m value.
Now apply point slope form to find the equation of the tangent line
y - y1 = m(x - x1)
y - 2 = 1(x - 1)
y - 2 = x - 1
y = x - 1 + 2
y = x + 1 is the equation of the tangent line.
The graph is shown below. I used GeoGebra to make the graph.
Answer:
23, 24, 25, 26, 27, 28, 29, or 30
22.5 ≤ p ≤ 30
Step-by-step explanation:
So we know that in 2/3 hours, Carlos can write 3 to 4 pages.
First, lets find how many 2/3's are in 5. Lets divide 5 by 2/3.
So there are 7.5 2/3's in 5.
Now, lets assume Carlos writes 4 pages per 2/3 hours consistently throughout that 5 hours. This would yield the maximum amount of pages Carlos can write in 5 hours.
7.5(4) = 30
So the maximum amount of pages Carlos can write in 5 hours is 30.
Now, lets assume Carlos writes 3 pages per 2/3 hours consistently throughout that 5 hours. This would yield the minimum amount of pages Carlos can write in 5 hours.
7.5(3) = 22.5
So the minimum amount of pages Carlos can write in 5 hours is 22.5.
Now we can write the information that we found as an inequality. Lets make p equal to the pages that Carlos can write in 5 hours.
22.5 ≤ p ≤ 30
Any value greater than to equal to 22.5 and less than or equal to 30 would be reasonable.
I hope you find my answer and explanation to be helpful. Happy studying.