Equation of the Tangent Line

[Jason76]

Find the equation of the tangent line to the curve at the given point:

\(\displaystyle f(x) = \sqrt{x}\) for point \(\displaystyle (9,3)\) - Basically there asking for the \(\displaystyle f'(9)\)

\(\displaystyle f(x) = x^{1/2}\)

\(\displaystyle f'(x) = (\dfrac{1}{2})x^{-1/2}\)

\(\displaystyle f'(x) = (\dfrac{1}{2})(9)^{-1/2}\) Based on "Order of Operations", what next?

 

[Bob Brown MSEE]

Find the equation of the tangent line to the curve at the given point:

\(\displaystyle f(x) = \sqrt{x}\) for point \(\displaystyle (9,3)\) - Basically there asking for the \(\displaystyle f'(9)\)

\(\displaystyle f(x) = x^{1/2}\)

\(\displaystyle f'(x) = (\dfrac{1}{2})x^{-1/2}\)

\(\displaystyle f'(x) = (\dfrac{1}{2})(9)^{-1/2}\) Based on "Order of Operations", what next?

Then get equation of the line with slope 1/6 going through (9,3)

 

[lookagain]

\(\displaystyle f'(x) = (\dfrac{1}{2})(9)^{-1/2}\) Based on "Order of Operations", what next?

Jason76,

before considering the post after your first post, back up to your comment here (highlighted above).

Do you, in fact, know how to evaluate that numerical expression using the Order of Operations?

 

[Jason76]

Jason76,

before considering the post after your first post, back up to your comment here (highlighted above).

Do you, in fact, know how to evaluate that numerical expression using the Order of Operations?

Evaluate the power

\(\displaystyle f(x) = \sqrt{x}\) for point \(\displaystyle (9,3)\)

\(\displaystyle f(x) = x^{1/2}\)

\(\displaystyle f'(x) = (\dfrac{1}{2})x^{-1/2}\)

\(\displaystyle f'(x) = (\dfrac{1}{2})(9)^{-1/2}\) - Evaluate the power

 

[srmichael]

Evaluate the power

\(\displaystyle f(x) = \sqrt{x}\) for point \(\displaystyle (9,3)\)

\(\displaystyle f(x) = x^{1/2}\)

\(\displaystyle f'(x) = (\dfrac{1}{2})x^{-1/2}\)

\(\displaystyle f'(x) = (\dfrac{1}{2})(9)^{-1/2}\) - Evaluate the power

Dude, Lookagain asked you if you know how to evaluate the expression and you simply rewrite what you had before! WTH?!

 

[Jason76]

Dude, Lookagain asked you if you know how to evaluate the expression and you simply rewrite what you had before! WTH?!

Sorry about that. Will work on later. Don't have a scientific calculator with me right now.

 

[JeffM]

Sorry about that. Will work on later. Don't have a scientific calculator with me right now.

You do not need a scientific calculator to evaluate

\(\displaystyle \dfrac{1}{2} * 9 ^{-(1/2)} = \dfrac{1}{2} * \dfrac{1}{9^{(1/2)}} = \dfrac{1}{2\sqrt{9}}.\) You can simplify even further if you try.