Question

Find the slope of the tangent line to the graph of f at the given point. f(x) = square root of x, at (36, 6)
A. 1/3
B. 12
C. 1/12

Answer 1

derivative of \(f(x)=\sqrt{x}\) is \(f'(x)=\frac{1}{2\sqrt{x}}\) memorize that one

Answer 2

\[f(x)=\sqrt{x}\]
\[f'(x) = \frac{1}{2\sqrt{x}}\]
\[evaluate \frac{1}{2*\sqrt{36}} = \frac{1}[\]

Answer 3

math teachers love to put it on quizzes and test, so while your classmates waste their time using the power rule, you are done in a second

Answer 4

1/12

Answer 5

Thank you everyone

Answer 6

what @Fonzy said
and don't forget
"the derivative of root x is one over two root x"
all day every day

Answer 7

Here's a more complete step so you can see if you are a visual type,
\[f(x) =\sqrt{x} \]
\[f(x) = x^{\frac{1}{2}} \] now apply the power rule.\[nx^{n-1}\]
\[f'(x) = \frac{1}{2}x^\frac{-1}{2}\]
\[f'(x) = \frac{1}{2\sqrt{x}}\]