Answer:
The equation of the tangent line to the curve at the given point is [tex]y = \frac{1}{14}(x - 49) + 7[/tex]
Step-by-step explanation:
Equation of the tangent line:
The equation of the tangent line to a function f(x) at a point [tex](x_0,y_0)[/tex] is given by:
[tex]y - y_0 = m(x - x_0)[/tex]
In which m is the slope, which is given by the derivative of f(x) at [tex]x_{0}[/tex]
y=√x, (49,7)
This means that [tex]x_0 = 49, y_0 = 7[/tex]
The derivative is:
[tex]y^{\prime} = \frac{1}{2\sqrt{x}}[/tex]
At [tex]x = 49[/tex]
[tex]m = y^{\prime} = \frac{1}{2\sqrt{49}} = \frac{1}{14}[/tex]
So
[tex]y - y_0 = m(x - x_0)[/tex]
[tex]y - 7 = \frac{1}{14}(x - 49)[/tex]
[tex]y = \frac{1}{14}(x - 49) + 7[/tex]
The equation of the tangent line to the curve at the given point is [tex]y = \frac{1}{14}(x - 49) + 7[/tex]
