Limits and Areas Given the function fx x3 2x 1 Let c1 1

Limits and Areas

Given the function f(x) = x^3 - 2x + 1. Let c_1 = - 1, c_2 = 0. a). Calculate f(c_1). b.) Determine the slopes of a secant lines connecting (x, f(x)) and {c_1, f(c_1)), using the x values [- 1.5, - 1.3, - 11, - 0.9, - 0.7, - 0.5]. c.) Calculate f(c_2).

Solution

f(c1) = f(-1) = 2

point (c1, f(c1) = (-1,2)

b)x , f(x) for all the points

(-1.5 , 5/8) , (-1.3 ,1.403) (-1.1,1.869) ,(-0.9,2.071) ,( -0.7, 2.057),(-0.5, 1.875)

slope for (x = -1.5 )= 2.75

for( x= -1.3) = 1.99

for (x = -1.1)   = 1.31

for (x = -0.9) = 0.71

for (x = -0.7) = 0.19

for (x = -0.5) = -0.25

c) c2= 0

so f(c2) = 1

further parts of question are not visible in the pic