Find the slope of the secant line?

The function f(x)=1.2x^3-32x^2+267x+575 below models the number of discharges from the​ military, f(x)of​ active-duty gay service members under the​ "don't ask,​ don't tell" policy x years after 1994.
Find the slope of the secant line from x(1)=0 to x(2)=4

1 Answer
May 7, 2018

# 158.2#.

Explanation:

The Reqd. Slope #m# of the secant line is given by,

#m=(f(x_2)-f(x_1))/(x_2-x_1)...........................(square)#.

We are given, #x_2=4, x_1=0. :. x_2-x_1=4............(square^1)#

#:. f(x_2)-f(x_1)=f(4)-f(0)#,

#={1.2(4)^3-32(4)^2+267(4)+575}-{575}#,

#=1.2(64)-32(16)+1068#,

#=76.8-512+1068#,

#:. f(x_2)-f(x_1)=632.8...................................(square^2)#.

Utilising #(square^1) and (square^2)" in "(square)#, we get,

#"The reqd. slope "m=632.8/4=158.2#.