Question

#13 problem 39 please show work so i can learn

ardo chierchia... 88 Marine Biology... High-speed photo... @ Vacation Re Question 13 Homework Problem 39 Find an equation of the tangent line to the graph of yr e-2 at the point (1, e-2) y=-2x + 7 y = 15x + 12 y=e+ (x + 1) y= *(-2x + 3) Question 14 Homework Problem 40 Find an equation of the tangent line to the graph of y=xe-* at the point (1, -1) • 1 y=2x+3 .y=e

Answer 1

e given y = e 2pt vihdoing at the point Cire?) find the tangent point plug x=1 into the equation for 7= è ? f6c=ė 21 = f = = compute the slope of f(x) =é ? in order to find the slope of the function taken the derivative of e 2x & Ce2x) = -282 = -2.62% -23 compute the slope of 16x=é atral: plug x=1 into the ean -2e 2x =-2.2-2'! Retine find the line with slope M = - 2 / 2 and passing through (1 ) compute the line equation y=mx+b for slope m= - 2 2 2 ? and boa and passing through (12)

compute the y-intercept plug the slope - 22 into y=mx+b f&l= ( x +b it all topiste plug in ca): x=1197 12 = (-22). It isolate b 1/2 = ( - 2 / 4) 1 tbt switch sidesnest (-2/4) .1 +3=162 = 2 2 tb=1 / 2 MEATFEfate acts . Add 2 2 por. both sides 용구들 터라를 b= 1 2 + 2 / 2 ba txurt the line equation yzmatb, where m = -2 2 and b = 3 / fc) 2 a 2 + 2 Paskyout y = fou ráz (-22+3) Ansois. P/thank you