40% of 120 is 48
1/4 of 200 is 50
1/4 of 200 is bigger.
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Answer:
x =3.1
![m = \frac{3.1^2 +3.1+6 -18}{3.1-3} = 7.1](https://tex.z-dn.net/?f=%20m%20%3D%20%5Cfrac%7B3.1%5E2%20%2B3.1%2B6%20-18%7D%7B3.1-3%7D%20%3D%207.1)
x =3.01
![m = \frac{3.01^2 +3.01+6 -18}{3.01-3} = 7.01](https://tex.z-dn.net/?f=%20m%20%3D%20%5Cfrac%7B3.01%5E2%20%2B3.01%2B6%20-18%7D%7B3.01-3%7D%20%3D%207.01)
x =2.9
![m = \frac{2.9^2 +2.9+6 -18}{2.9-3} = 6.9](https://tex.z-dn.net/?f=%20m%20%3D%20%5Cfrac%7B2.9%5E2%20%2B2.9%2B6%20-18%7D%7B2.9-3%7D%20%3D%206.9)
x =2.99
![m = \frac{2.99^2 +2.99+6 -18}{2.99-3} = 6.99](https://tex.z-dn.net/?f=%20m%20%3D%20%5Cfrac%7B2.99%5E2%20%2B2.99%2B6%20-18%7D%7B2.99-3%7D%20%3D%206.99)
Based on the results we can conclude this condition:
![y'(3) = 7](https://tex.z-dn.net/?f=%20y%27%283%29%20%3D%207)
And the slope would be given by:
Step-by-step explanation:
For this case we have defined the point P=(3,18) and Q= (x, x^2 +x+6) and we want to find the slope of the secant for the line PQ for a list of values.
The slope for the secant would be given by this formula:
![m = \frac{Q_y -P_y}{Q_x -P_x}](https://tex.z-dn.net/?f=%20m%20%3D%20%5Cfrac%7BQ_y%20-P_y%7D%7BQ_x%20-P_x%7D)
And if we replace the values for the points we got:
![m = \frac{x^2 +x+6 -18}{x-3}](https://tex.z-dn.net/?f=%20m%20%3D%20%5Cfrac%7Bx%5E2%20%2Bx%2B6%20-18%7D%7Bx-3%7D)
So now we just need to replace the different values for x
x =3.1
![m = \frac{3.1^2 +3.1+6 -18}{3.1-3} = 7.1](https://tex.z-dn.net/?f=%20m%20%3D%20%5Cfrac%7B3.1%5E2%20%2B3.1%2B6%20-18%7D%7B3.1-3%7D%20%3D%207.1)
x =3.01
![m = \frac{3.01^2 +3.01+6 -18}{3.01-3} = 7.01](https://tex.z-dn.net/?f=%20m%20%3D%20%5Cfrac%7B3.01%5E2%20%2B3.01%2B6%20-18%7D%7B3.01-3%7D%20%3D%207.01)
x =2.9
![m = \frac{2.9^2 +2.9+6 -18}{2.9-3} = 6.9](https://tex.z-dn.net/?f=%20m%20%3D%20%5Cfrac%7B2.9%5E2%20%2B2.9%2B6%20-18%7D%7B2.9-3%7D%20%3D%206.9)
x =2.99
![m = \frac{2.99^2 +2.99+6 -18}{2.99-3} = 6.99](https://tex.z-dn.net/?f=%20m%20%3D%20%5Cfrac%7B2.99%5E2%20%2B2.99%2B6%20-18%7D%7B2.99-3%7D%20%3D%206.99)
Based on the results we can conclude this condition:
![y'(3) = 7](https://tex.z-dn.net/?f=%20y%27%283%29%20%3D%207)
And the slope would be given by:
Answer:
a. 8
b. 248
Step-by-step explanation:
first, find the derivative:
-2x^2 + 32x + 120
= -4x + 32
then, have that equal 0
-4x + 32 = 0
32 = 4x
8 = x
answer a: 8
plug in answer a into the original equation
-2(8)^2 + 32(8) +120
answer b: 248