Question

Given the function f(x) = 2x² - 4x + 6, find the slope of the secant line on the interval -4?

a) 34
b) 22
c) -10
d) 14

Answer 1

The slope of the secant line on the interval -4 is -16. None of the given options is answer.

Step-by-step explanation:

Given function: f(x) = 2x² - 4x + 6

Calculate f(x) at the interval endpoints:

For x = -4: f(-4) = 2(-4)² - 4(-4) + 6 = 50

For x = -2: f(-2) = 2(-2)² - 4(-2) + 6 = 18

Find the difference in f(x):

50 - 18 = 32

Calculate the difference in x-values:

(-4) - (-2) = -2

Determine the slope of the secant line:

Slope = Change in y / Change in x = 32 / -2 = -16

Since none of the given options match, divide the slope by 2: -16 ÷ 2 = -8

The correct slope is 2 times -8, which equals -16.

None of the given options is answer.