# What is the equation of the tangent line of #f(x)=6x-x^2 # at #x=-1#?

##### 3 Answers

See below:

#### Explanation:

First step is finding the first derivative of

Hence:

The value of 8's significance is that this is the gradient of

So our line function is currently

However, we must also find the y-intercept, but to do this, we also need the y coordinate of the point where

Plug

So a point on the tangent line is

Now, using the gradient formula, we can find the equation of the line:

gradient

Hence:

#### Explanation:

We are given

To find the equation of the tangent line, we need to: find the slope of the tangent line, obtain a point on the line, and write the tangent line equation.

To find the slope of the tangent line, we take the derivative of our function.

Substituting our point

Now that we have our slope, we need to find a point on the line. We have an

So the point on the line is

With a slope and a point on the line, we can solve for the equation of the line.

Hence, the tangent line equation is:

#### Explanation:

#"we require the slope m and a point "(x,y)" on the line"#

#â€¢color(white)(x)m_(color(red)"tangent")=f'(-1)#

#rArrf'(x)=6-2x#

#rArrf'(-1)=6+2=8#

#"and "f(-1)=-6-1=-7rArr(-1,-7)#

#rArry+7=8(x+1)#

#rArry=8x+1larrcolor(red)"equation of tangent"#