Question

Find an equation of the tangent line to the curve at the given point. y=√x, (49,7) To find the equation of a line, we need the slope of the line and a

Answer 1

The equation of the tangent line to the curve at the given point is
`y = (1)/(14)(x - 49) + 7`

Explanation:

Equation of the tangent line:

The equation of the tangent line to a function f(x) at a point
`(x_0,y_0)` is given by:

`y - y_0 = m(x - x_0)`

In which m is the slope, which is given by the derivative of f(x) at
`x_(0)`

y=√x, (49,7)

This means that
`x_0 = 49, y_0 = 7`

The derivative is:

`y^(\prime) = (1)/(2√(x))`

At
`x = 49`

`m = y^(\prime) = (1)/(2√(49)) = (1)/(14)`

So

`y - y_0 = m(x - x_0)`

`y - 7 = (1)/(14)(x - 49)`

`y = (1)/(14)(x - 49) + 7`

The equation of the tangent line to the curve at the given point is
`y = (1)/(14)(x - 49) + 7`