# How do you find the tangent line to the curve #y=x^3-9x# at the point where #x=1#?

##### 2 Answers

Apr 21, 2018

#### Explanation:

Given:

Let

So, the point we are targeting is

To find the slope of the tangent line there, we must differentiate

At

So, the slope of the tangent line is

Now, we use the point-slope formula to compute the equation, that is,

#(x_0,y_0)# are the original coordinates

Therefore, we get,

A graph shows it:

Apr 21, 2018

#### Explanation:

#â€¢color(white)(x)m_(color(red)"tangent")=dy/dx" at x = 1"#

#rArrdy/dx=3x^2-9#

#rArrdy/dx(x=1)=3-9=-6#

#rArry(x=1)=1-9=-8rArr(1,-8)#

#"using "m=-6" and "(x_1,y_1)=(1,-8)#

#y+8=-6(x-1)#

#rArry=-6x-2larrcolor(red)"equation of tangent"#