Question

Find the slope of the tangent line to the graph of f at the given point.

Answer 1

How can you find the slope of a function at a given point? Slope is the rate of change of a function. How is rate of change defined?

The change in y, divided by the change in x. \( \frac{\Delta y}{\Delta x} \)

Perform some infinitesimal magic and we stumble upon \( \frac{dy}{dx} \).

Our function is \( y=\sqrt{x} \).
The derivative of this is \( y' = \frac{1}{2\sqrt{x}} \).
At \(x=36\), \( y' = \frac{1}{2\sqrt{36}} = \frac{1}{(2)(6)} = \frac{1}{12}. \)

Answer 2

thank you for explainging this(: