Answer:
-4g^4 -3g^3 + 4g^2 +5g +3
Step-by-step explanation:
g^2 + -4g^4 +5g +9 -3g^3 + 3g^2 -6
-4g^4 -3g^3 + 4g^2 +5g +3
Inc on (-inf,0)
Dec on (0,inf)
Answe
Given,
f(x) = 49 − x² from x = 1 to x = 7
n = 4

For x= 1
f(x₀) = 49 - 1^2 = 48
x = 2.5
f(x₁) = 42.75
x = 4
f(x₂) = 49 - 4^2 = 33
x = 5.5
f(x₃) = 49 - 5.5^2 = 18.75
x = 7
f(x₄) = 49 - 7^2 = 0
We have to evaluate the function on therigh hand point
![A = \Delta x [f(x_1)+f(x_2)+f(x_3)+f(x_4)]](https://tex.z-dn.net/?f=A%20%3D%20%5CDelta%20x%20%5Bf%28x_1%29%2Bf%28x_2%29%2Bf%28x_3%29%2Bf%28x_4%29%5D)
![A = 1.5 [42.75+33+18.75+0]](https://tex.z-dn.net/?f=A%20%3D%201.5%20%5B42.75%2B33%2B18.75%2B0%5D)

For Area for left hand sum
![A = \Delta x [f(x_0)+f(x_1)+f(x_2)+f(x_3)]](https://tex.z-dn.net/?f=A%20%3D%20%5CDelta%20x%20%5Bf%28x_0%29%2Bf%28x_1%29%2Bf%28x_2%29%2Bf%28x_3%29%5D)
![A = 1.5 [48+42.75+33+18.75]](https://tex.z-dn.net/?f=A%20%3D%201.5%20%5B48%2B42.75%2B33%2B18.75%5D)

(x+2y+z) (x-2y-z)
= x^2 - 2xy - xz + 2xy - 4y^2 - 2yz + xz - 2yz - z^2 = x^2 - 4y^2 - 4yz -z^2
Hope it helped!