Q:

Numerically estimate the slope of y = f(x) at r = a. 1. f(x) = x^2 - 2x, a = 2 2. f(x) = sin 2x, a = 0

Accepted Solution

A:
Answer:1. Slope at a=2 is 2.2. Slope at a=0 is 2.Step-by-step explanation:We need to find the slope of y = f(x) at x = a. 1.The given function is[tex]f(x)=x^2-2x[/tex]It can be written as[tex]y=x^2-2x[/tex]Differentiate with respect to x.[tex]y'=2x-2[/tex]Substitute x=2 to find the slope of y = f(x) at a=2.[tex]y'=2(2)-2[/tex][tex]y'=4-2[/tex][tex]y'=2[/tex]Therefore the slope of function at a=2 is 2.2.The given function is[tex]f(x)=\sin 2x[/tex]It can be written as[tex]y=\sin 2x[/tex]Differentiate with respect to x.[tex]y'=2\cos 2x[/tex]Substitute x=0 to find the slope of y = f(x) at a=0.[tex]y'=2\cos 2(0)[/tex][tex]y'=2(1)[/tex][tex]y'=2[/tex]Therefore the slope of function at a=0 is 2.