Answer: y = –8x + 16
Explanation
Given
[tex]g\mleft(x\mright)=\left(x-4\right)^2[/tex]First, we have to know the y-intercept, which is the point where x = 0:
[tex]g(0)=(0-4)^2[/tex][tex]g(0)=16[/tex]Thus, the y-intercept is (0, 16).
Next, we have to get the derivative of the function, as the tangent line is the derivative:
[tex]\frac{dg(x)}{dx}=2(x-4)[/tex]Then, we have to compute the slope:
[tex]m=-8[/tex]Finally, we find the line in the slope-intercept form (y = mx + b):
[tex]b=16[/tex]Thus:
[tex]y=-8x+16[/tex]