Answer :
Answer: y=1/8*x+2
Step-by-step explanation:
The equation of any tangent line is y=a*x+b (1)
To the equation of the tangent line we have to find the coefficients a and b and the to substitute them to equation (1).
As we know a=y'(x0) ( where x0=16)
So y'(x)= (√ (x) )' = 1/(2*√x)
a=y'(x0)= 1/(2*√16)=1/(2*4)=1/8
So lets substitute a in equation (1):
y=1/8 *x+b
Now we have to find b
We know that the point (16, 4) belongs to the tangent line.
That means
4=1/8*16+b => 4=2+b => b=2
SO the equation of the tangent line is y=1/8*x+2