Question

Find an equation of the tangent line to the curve at the given point.

y = √ (x) , (16, 4)

Answer 1

Answer: y=1/8*x+2

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