the slope of the tangent line to the curve y=square root of x at x=1 is defined by m=lim (h gt 0) square root of 1+h -1/h. compute the slope m.


graph y=square root of x and the line with slope m throught the point (1,1)

Expert Answers

An illustration of the letter 'A' in a speech bubbles

You need to find the derivative of the function `f(x) = y = sqrt x ` at x=1 such that:

`f'(x) = 1/(2sqrt x)`

You need to substitute 1 for x in f'(x) such that:

`f'(1) = 1/(2sqrt 1) =gt f'(1) = 1/2 `

You need to write the equation of the tangent line to the curve `y = sqrt x` , at the point (1,1) such that:

`y - f(1) = f'(1)(x-1)`

You need to evaluate f(1) such that:

`f(1) = sqrt 1 = 1`

`y - 1 = (1/2)(x - 1)`

`y = x/2 - 1/2 + 1`

`y = x/2 + 1/2`

Hence, evaluating the slope of the tangent line at the curve `y =sqrt x` , at point (1,1) yields `m = f'(1)= 1/2` .

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial