# How do you find the slope of the graph g(t)=2+3cost at (pi,-1)?

Dec 14, 2016

See explanation.

#### Explanation:

To find a slope of a graph at a specified point you have to calculate the value of first derivative at this point.

If $g \left(t\right) = 2 + 3 \cos t$ then:

$g ' \left(t\right) = 3 \cdot \left(- \sin t\right) = - 3 \sin t$

Now at the point ${x}_{0} = \pi$ the derivative is:

$g ' \left(\pi\right) = - 3 \sin \pi = - 3 \cdot 0 = 0$

The slope of the graph at $\left(\pi , - 1\right)$ is $0$.