Respuesta :
Alright, lets get started.
We have given a curve y, and a point P.
[tex] y = 7x + 9 cosx [/tex]
The derivative of the curve is the slope of the tangent line.
We will find the derivative of the given function.
[tex] \frac{dy}{dx} = \frac{d}{dx}(7x + 9 cos x) [/tex]
[tex] \frac{dy}{dx} = 7 + 9 (-sin x) [/tex]
[tex] \frac{dy}{dx} = 7 - 9 sin x [/tex]
Putting the value as x = 0 because P (0,9)
[tex] \frac{dy}{dx} = 7 - 9 sin 0 [/tex]
As sin 0 = 0
[tex] \frac{dy}{dx} = 7 - 0 [/tex]
[tex] \frac{dy}{dx} = 7 [/tex]
The equation of tangent will be : [tex] y =mx + c [/tex] where m is slope
[tex] y = 7 x + c [/tex]
Putting the value of (x,y) as (0,9), we could find the value of c
[tex] 9 = 7 * 0 + c [/tex]
c = 9
Hence the equation of tangent will be :
[tex] y = 7 x + 9 [/tex]
Answer
Hope it will help :)
