Question

Find an equation of the tangent line to the curve at the given point. y = 7x + 9 cos(x), p = (0, 9)

Answer 1

Alright, lets get started.

We have given a curve y, and a point P.

$y = 7x + 9 cosx$

The derivative of the curve is the slope of the tangent line.

We will find the derivative of the given function.

$\frac{dy}{dx} = \frac{d}{dx}(7x + 9 cos x)$

$\frac{dy}{dx} = 7 + 9 (-sin x)$

$\frac{dy}{dx} = 7 - 9 sin x$

Putting the value as x = 0 because P (0,9)

$\frac{dy}{dx} = 7 - 9 sin 0$

As sin 0 = 0

$\frac{dy}{dx} = 7 - 0$

$\frac{dy}{dx} = 7$

The equation of tangent will be : $y =mx + c$ where m is slope

$y = 7 x + c$

Putting the value of (x,y) as (0,9), we could find the value of c

$9 = 7 * 0 + c$

c = 9

Hence the equation of tangent will be :

$y = 7 x + 9$

Answer

Hope it will help :)