Question

suppose $y = -2x - 4$ is the equation of the tangent line to the graph of a function $y = g(x)$ at $x = -1.5$. find $g(-1.5)$ and $g(-1.5)$. $g(-1.5) = \square$ $g(-1.5) = \square$

Explanation:

Step1: Calculate $g(-1.5)$

Substitute $x=-1.5$ into tangent line equation:
$y = -2(-1.5) - 4$
$y = 3 - 4 = -1$
Since the tangent line touches $g(x)$ at $x=-1.5$, $g(-1.5)$ equals this $y$-value.

Step2: Identify $g'(-1.5)$

The derivative $g'(x)$ at a point is the slope of the tangent line at that point. The tangent line $y=-2x-4$ has slope $-2$, so $g'(-1.5) = -2$.

Answer:

$g(-1.5) = -1$
$g'(-1.5) = -2$