Question

Find the slope and an equation of the tangent line to this equation (sqrtx)+(1/(sqrtx))

Answer 1

Would you mind defining your function, either in the form f(x) = (expression in x), or as an implicit function, such as

y*sqrt(x) =1/(sqrt(x)?

your sqrt(x) + (1/sqrt(x) is not an equation, even though you label it as one.

Answer 2

Once you've cleared this up, approaching the problem solving you've posed will be relatively straightforward.

Answer 3

f(x)=sqrt(x)+(1/(sqrt(x))

Answer 4

Thank you, Alex. That's so much clearer now.

To find the equation of the tangent line to this function f(x) at point (a,b), we find the derivative f '(x) (which, in turn, represents the slope of the tangent line); then the equation of the tangent line, from the point-slope formula, becomes y-b = m (x -a).

Answer 5

Would you please find f '(x) now?

Answer 6

keeping in mind that \(\large \bf \sqrt{x}+\cfrac{1}{\sqrt{x}}\implies x^{\frac{1}{2}}+x^{-\frac{1}{2}}\)

Answer 7

Thanks, JDoe! So f(x) = x^(1/2) + x^(-1/2). Alex, please find f '(x) now.

Answer 8

(x-1)/(2x^(3/2)) ?