Question

If we have the curve y = sqrt(x), find the y value and the slope of the curve when x = 36. y = 6 Correct: Your answer is correct. slope = 1/12 Correct: Your answer is correct. Hence, find the equation of the tangent line to the curve at x = 36, writing your answer in the form y = mx + c. What are the values of m and c?

m =
c =

Answer 1

Equation of tangent of curve at x = 36:

1)
`y = (x)/(12) + 3`

2
`y = (-x)/(12) - 3`

Explanation:

We are given the following information:

`y = √(x)`

Value of curve when x = 36:

`y = √(36) = \pm 6`

Thus,
`y = \pm6`, when x = 6.

Slope of curve, m =

`(dy)/(dx) =(d(√(x)))/(dx)=(1)/(2√(x))`

At x = 36,

slope of curve =

`(1)/(2* √(36))\\\\m=(1)/(12),(-1)/(12)`

Equation of tangent of curve at x = 36:

`(y-y_1) = m(x-x_1)`

`= (y-(\pm 6)) = (\pm(1)/(12) )(x - 36)`

Thus, equation of tangents are:

1)

`(y-6) = (1)/(12)(x-36)\\12(y-6) = x-36\\y = (x)/(12) + 3`

Comparing to
`y = mx + c`, we get
`m = (1)/(12)` and
`c =3`

2)

`(y+6) = (-1)/(12)(x-36)\\12(y+6) = -x+36\\y = (-x)/(12) - 3`

Comparing to
`y = mx + c`, we get
`m = (-1)/(12)` and
`c =-3`