Answer:
y = 6.20 + 12.4(x - pi/4)
Step-by-step explanation:
dy/dx = 2e^x secx + 2e^x secx * tanx= 2e^x secx (1 + tanx)
At x = pi/4, use sec(pi/4) = [tex]\sqrt{2}[/tex]. tan(pi/4) =1
so dy/dx = 2e^(pi/4) * [tex]\sqrt{2}[/tex] * (1 + 1) = [tex]4 \sqrt{2} e^{\pi/4}[/tex] ≈ 12.4 (This is the slope of the tangent line)
When x = pi/4, y = 2e^(pi/4) * [tex]\sqrt{2}[/tex] = [tex]2 \sqrt{2} e^{\pi/4}[/tex]= 6.20
Then the equation of the tangent line is
y = 6.20 + 12.4(x - pi/4)
