Question

Given f(x) = -2x^2 + 4, determine the slope of the secant line over the interval [-1, 2].

Answer 1

Answer:  -2

Step-by-step explanation:

We know that the slope of a secant line over a interval [a,b] is given by :-

$m=\dfrac{f(b)-f(a)}{b-a}$

Given f(x) =$-2x^2 + 4$

Then, the slope of the secant line over the interval [-1, 2] is given by :-

$m=\dfrac{f(2)-f(-1)}{2-(-1)}\\\\=\dfrac{(-2(2)^2+4)-(-2(-1)^2+4)}{2+1}\\\\=\dfrac{(-2(4)+4)-(-2(1)+4)}{3}\\\\=\dfrac{(-8+4)-(-2+4)}{3}\\\\=\dfrac{-4-2}{3}\\\\=\dfrac{-6}{3}\\\\=-1$

Hence, the slope of the secant line over the interval [-1, 2] is -2.