for interval:  0.5<=b<=2  fine the equation of tangent for the following function:  f(x) = x + 1/x

Expert Answers info

sciencesolve eNotes educator | Certified Educator

calendarEducator since 2011

write5,349 answers

starTop subjects are Math, Science, and Business

You need to remember that you may find the equation of the tangent line to the graph of `f(x),`  at a point `x = x_0` , using the following formula such that:

`y - f(x_0) = f'(x_0)(x - x_0)`

Selecting a value in the given interval `[0.5,2],` `x_0 = 1` , the equation of the tangent line is:

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

You need to find `f'(x)`  such that:

`f'(x) = (x + 1/x)' => f'(x) = 1 - 1/x^2`

Substituting 1 for x yields:

`f'(1) = 1 - 1/1 = 1-1 = 0`

You need to evaluate `f(1) ` such that:

`f(1) = 1 + 1/1 = 2`

Substituting 2 for `f(1)`  and 0 for `f'(1)`  yields:

`y - 2 = 0*(x - 1) => y = 2`

Hence, evaluating the equation of the tangent line to the graph of the given function, at a point in the given interval `[0.5,2]`  yields `y = 2` .

check Approved by eNotes Editorial

Unlock This Answer Now