Question

Find the EQUATION OF THE TANGENT to g(x)=(x-4)^2 at it’s y-intercept. Please use an appropriate limit, much appreciated!

Answer 1

Answer: y = –8x + 16

Step-by-step explanation

Given

`g\mleft(x\mright)=\left(x-4\right)^2`

First, we have to know the y-intercept, which is the point where x = 0:

`g(0)=(0-4)^2`
`g(0)=16`

Thus, the y-intercept is (0, 16).

Next, we have to get the derivative of the function, as the tangent line is the derivative:

`(dg(x))/(dx)=2(x-4)`

Then, we have to compute the slope:

`m=-8`

Finally, we find the line in the slope-intercept form (y = mx + b):

`b=16`

Thus:

`y=-8x+16`