Math $2413$: Worksheet $4$

Page $3$ of $4$

$2.[$DM$1]$ Consider the function $f(x)$ graphed below. For the questions, recall that the derivative of $f$ at a point $a$ is the SLOPE of the TANGENT LINE that passes through the point $(a,f(a)).$ Thus, sketch tangent lines at the designated points and study the slopes of the tangent lines.

a$.$ Give two $x-$values where $f^{\text{'}}(x)=0,$ that is where the derivative of $f$ is zero, that is$,$ where the slope of the tangent line is zero. $($Estimate if necessary.$)$

b$.$ Give two $x-$values where $f^{\text{'}}(x)>0,$ that is where the derivative of $f$ is positive.

c$.$ Give two $x-$values where that is where the derivative of $f$ is negative.

d$.$ Arrange the following values$/$numbers from least to greatest: $f^{\text{'}}(-4)f^{\text{'}}(-1)f^{\text{'}}(4)$

$f^{\text{'}}(8)$