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The derivative of a function
g is given by

g^(')(x)=3sin(x)+ln(x)". "
How many relative extremum points does the graph of
g have on the interval
1 < x < 5 ?
Use a graphing calculator.
Choose 1 answer:
(A) One
(B) Two
(C) Three
(D) Four

The derivative of a function $g$ is given by $\newline$ $g^{\prime}(x)=3 \sin (x)+\ln (x) \text {. }$ $\newline$ How many relative extremum points does the graph of $g$ have on the interval $1<x<5$ ? $\newline$ Use a graphing calculator. $\newline$ Choose $1$ answer: $\newline$ (A) One $\newline$ (B) Two $\newline$ (C) Three $\newline$ (D) Four

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Write equations of cosine functions using properties

Full solution

Q. The derivative of a function

g

is given by

\newline

g^{\prime}(x)=3 \sin (x)+\ln (x) \text {. }

\newline

How many relative extremum points does the graph of

g

have on the interval

1<x<5

?

\newline

Use a graphing calculator.

\newline

Choose

1

answer:

\newline

(A) One

\newline

(B) Two

\newline

(C) Three

\newline

(D) Four

Find Extremum Points: To find relative extremum points, we need to find where the derivative $g'(x) = 3\sin(x) + \ln(x)$ is equal to $0$ or undefined.
Consider Interval: Since $\ln(x)$ is undefined for $x \leq 0$ , we only consider where $3\sin(x) + \ln(x) = 0$ on the interval $1 < x < 5$ .
Graphing Calculator: Use a graphing calculator to plot $y = 3\sin(x) + \ln(x)$ and look for the $x$ -values where the graph crosses the $x$ -axis between $1$ and $5$ .
Identify Extremum Points: The graph of $y = 3\sin(x) + \ln(x)$ crosses the $x$ -axis twice between $1$ and $5$ , indicating two relative extremum points.

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