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

Answer:

Equation of tangent of curve at x = 36:    

1)$y = \frac{x}{12} + 3$ 

2$y = \frac{-x}{12} - 3$     

Step-by-step explanation:

We are given the following information:

$y = \sqrt{x}$

Value of curve when x =  36:

$y = \sqrt{36} = \pm 6$

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

Slope of curve, m =

$\frac{dy}{dx} =\frac{d(\sqrt{x})}{dx}=\frac{1}{2\sqrt{x}}$

At x = 36,

slope of curve =

$\frac{1}{2\times \sqrt{36}}\\\\m=\frac{1}{12},\frac{-1}{12}$

Equation of tangent of curve at x = 36:

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

$= (y-(\pm 6)) = (\pm\frac{1}{12} )(x - 36)$

Thus, equation of tangents are:

1)

$(y-6) = \frac{1}{12}(x-36)\\12(y-6) = x-36\\y = \frac{x}{12} + 3$

Comparing to $y = mx + c$, we get $m = \frac{1}{12}$ and $c =3$

2)

$(y+6) = \frac{-1}{12}(x-36)\\12(y+6) = -x+36\\y = \frac{-x}{12} - 3$

Comparing to $y = mx + c$, we get $m = \frac{-1}{12}$ and $c =-3$