Evaluate the sum using the given information.
-$x _ { 1 } = - 4 , x _ { 2 } = 0 , x _ { 3 } = 2 , x _ { 4 } = 5$, and $\Delta x = - 0.9 ; f ( x ) = 3 x ^ { 2 } - x$
$\sum _ { \mathrm { i } = 1 } ^ { 4 } \mathrm { f } \left( \mathrm { x } _ { \mathrm { i } } \right) \Delta \mathrm { x }$
A) $- 475.2$
B) $- 117.8$
C) $- 118.8$
D) $- 20.7828$

Question

Quizplus · Accepted Answer

To find the sum, we calculate $f(x_i)$ for each $x_i$ and multiply by $\Delta x$, then sum these products. $f(x) = 3x^2 - x$, so:- $f(-4) = 3(-4)^2 - (-4) = 48 + 4 = 52$- $f(0) = 3(0)^2 - 0 = 0$- $f(2) = 3(2)^2 - 2 = 12 - 2 = 10$- $f(5) = 3(5)^2 - 5 = 75 - 5 = 70$Summing these with $\Delta x = -0.9$:- $52(-0.9) + 0(-0.9) + 10(-0.9) + 70(-0.9) = -46.8 - 0 - 9 - 63 = -118.8$.

Evaluate the Sum Using the Given Information x1=−4,x2=0,x3=2,x4=5x _ { 1 } = - 4 , x _ { 2 } = 0 , x _ { 3 } = 2 , x _ { 4 } = 5x1​=−4,x2​=0,x3​=2,x4​=5

Evaluate the Sum Using the Given Information $x _ { 1 } = - 4 , x _ { 2 } = 0 , x _ { 3 } = 2 , x _ { 4 } = 5$