Expert Answer to "How do you find the equation of the..."

Randy Dean

Answered question

2022-02-13

How do you find the equation of the line tangent to the graph of

{(2 x + 3)}^{\frac{1}{2}}

at the point x=3?

prudomiajpt

Beginner2022-02-14Added 15 answers

First use the chain rule to get the derivative:
Let:

y = {(2 x + 3)}^{\frac{1}{2}}

y^{'} = \frac{1}{2} {(2 x + 3)}^{- \frac{1}{2}} \times 2

= \frac{1}{\sqrt{2 x + 3}}

If x=3:

y^{'} = \frac{1}{\sqrt{9}} = \frac{1}{3}

The equation of the line is of the form:
y=mx+c
So

m = \frac{1}{3}

If x=3 then

y = \sqrt{(2 \times 3) + 3} = 3

3 = \frac{1}{3} \times 3 + c

c=3-1=2
So the equation

\Rightarrow

y = \frac{x}{3} + 2

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