Finding Slope with Desmos and Table

[karush]

ok attemped to do this desmos but was sondering if there is away to get these slope in a 3rd column in the table with $m=\dfrac{\delta y}{\delta x}$

 

[topsquark]

Do you need to use Desmos? It's easy enough to calculate: [math]\dfrac{d(sec(x)}{dx} = tan(x)~sec(x)[/math]

-Dan

 

[karush]

I just thot it would be cute if I did,,

 

[HOI]

How is the derivative relevant at all? The problem does not ask for the slope of the tangent line, it asks for the slope of the "secant" line, through P= (0.5, 0) and $Q= (x, cos(\pi x))$ for various values of x.

For (i) x= 0 so Q= (0, 1) and the slope of the slope of the secant line is $\frac{0- 1}{0.5- 0}= -2$. For (ii) x= 0.4 so Q=(0.4, 0.9998) so the slope of the secant line is $\frac{0- 0.9998}{.5- .4}= -9.998$ (to three decimal places).

What do you get for the others?