Question

Extra Credit (5 points) The left-hand graph shows the DERIVATIVE $k'$ of some function $k$. The derivative $k'(x)$ The following questions are about the original function $k(x)$, not the graphed $k'(x)$. a. At what value(s) of $x$ does $k$ have a local maximum or minimum? If none, say so. Write some words to explain how you know that these $x$-values correspond to a local max or min (or not). Local Max: $x =$ Local Min: $x =$ b. At what values of $x$ does $k$ have inflection points? If none, say so. Write some words to explain how you know that these $x$-values correspond to inflection points (or not). Inflection points: $x =$ c. Sketch the graph of the original function $k(x)$ on the axes to the left of the derivative, using the fact that $k(-7) = 1$. Your sketch does not have to be to scale, but it should show the right information regarding increasing/decreasing/max/min/concavity/inflection points. Mark important values on the $x$- and $y$-axes.

          Extra Credit (5 points) The left-hand graph shows the DERIVATIVE $k'$ of some function $k$.
The derivative $k'(x)$
The following questions are about the original function $k(x)$, not the graphed $k'(x)$.
a. At what value(s) of $x$ does $k$ have a local maximum or minimum? If none, say so. Write some words
to explain how you know that these $x$-values correspond to a local max or min (or not).
Local Max: $x =$
Local Min: $x =$
b. At what values of $x$ does $k$ have inflection points? If none, say so. Write some words to explain how
you know that these $x$-values correspond to inflection points (or not).
Inflection points: $x =$
c. Sketch the graph of the original function $k(x)$ on the axes to the left of the derivative, using the fact
that $k(-7) = 1$. Your sketch does not have to be to scale, but it should show the right information
regarding increasing/decreasing/max/min/concavity/inflection points. Mark important values on the
$x$- and $y$-axes.

Extra Credit (5 points) The left-hand graph shows the DERIVATIVE k' of some function k.
The derivative k'(x)
The following questions are about the original function k(x), not the graphed k'(x).
a. At what value(s) of x does k have a local maximum or minimum? If none, say so. Write some words
to explain how you know that these x-values correspond to a local max or min (or not).
Local Max: x =
Local Min: x =
b. At what values of x does k have inflection points? If none, say so. Write some words to explain how
you know that these x-values correspond to inflection points (or not).
Inflection points: x =
c. Sketch the graph of the original function k(x) on the axes to the left of the derivative, using the fact
that k(-7) = 1. Your sketch does not have to be to scale, but it should show the right information
regarding increasing/decreasing/max/min/concavity/inflection points. Mark important values on the
x- and y-axes.

Added by Carl D.

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