Derivatives help URGENT

Question

Given f(x) = -2x2 + 4, determine the slope of the secant line over the interval [-1, 2].

Answer 1

f(x) = -2x² + 4

f(-1) = -2(-1)² + 4

f(-1) = 2

 

f(2) = -2(2)² + 4

f(2) = -4

 

Now find the slope of the line through (-1, 2) and (2, -4).

Answer 2

f(x) = -2x²+4; x = - 1 to x = 2

 

f(-1) = -2*-1^2 + 4 = 2

 

f(2) = -2*2^2 + 4 = -4

 

So the two points on the secant line that intersect with the curve are: (-1,2) and (2,-4). 

 

Slope = ΔY/ΔX = (-4 - 2)/(2 - (-1)) = -6/3 = -2.