Question

Find an equation of the tangent line to the curve at the given point ? y= (sqrt x) , (49,7)

Answer 1

First we can find the slope of your tangent calculating the derivative of your function and substituting the value `x=49` in it:
1) `f(x)=sqrt(x)`
`f'(x)=1/(2sqrt(x))`
2) for `x=49` you get:
`f'(49)=1/(2sqrt(49))=1/14`
3) the equation of the tangent with slope `m=1/14` and passing through (`x_0=49, y_0=7`) can be written as:
`y-y_0=m(x-x_0)`
`y-7=1/14(x-49)`
`y=x/14+7/2`

Graphically: