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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 g is given by\newlineg′(x)=3sin⁡(x)+ln⁡(x).  g^{\prime}(x)=3 \sin (x)+\ln (x) \text {. } \newlineHow many relative extremum points does the graph of g g have on the interval \( 1

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Q. The derivative of a function g g is given by\newlineg′(x)=3sin⁡(x)+ln⁡(x).  g^{\prime}(x)=3 \sin (x)+\ln (x) \text {. } \newlineHow many relative extremum points does the graph of g g have on the interval 1<x<5 1<x<5 ?\newlineUse a graphing calculator.\newlineChoose 11 answer:\newline(A) One\newline(B) Two\newline(C) Three\newline(D) Four
  1. Find Extremum Points: To find relative extremum points, we need to find where the derivative g′(x)=3sin⁡(x)+ln⁡(x)g'(x) = 3\sin(x) + \ln(x) is equal to 00 or undefined.
  2. Consider Interval: Since ln⁡(x)\ln(x) is undefined for x≤0x \leq 0, we only consider where 3sin⁡(x)+ln⁡(x)=03\sin(x) + \ln(x) = 0 on the interval 1 < x < 5.
  3. Graphing Calculator: Use a graphing calculator to plot y=3sin⁡(x)+ln⁡(x)y = 3\sin(x) + \ln(x) and look for the xx-values where the graph crosses the xx-axis between 11 and 55.
  4. Identify Extremum Points: The graph of y=3sin⁡(x)+ln⁡(x)y = 3\sin(x) + \ln(x) crosses the xx-axis twice between 11 and 55, indicating two relative extremum points.

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