Question

find tangent line equation to the curve at the given point:

y= 7e^x cos(x) P=(0,7)

Answer 1

dy/dx = -7 e^x sin x + 7 e^x cos x

= 7 e^x (cos x - sin x)

at (0,7)
dy/dx = m the slope = 7 e^0 (cos 0 - sin 0)
= 7
so y = 7x+b

at(0,7)
7 = 7(0) + b
so b = 7
and
y = 7 x + 7
or
y = 7(x+1)