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![The derivative of a function
f is given by
f^(')(x)=e^(x)-x^(3).
On which intervals is the graph of
f decreasing?
Use a graphing calculator.
Choose 1 answer:
(A)
[1.857,4.536]
(B)
(-oo,1.857] and
[4.536,oo)
(C)
(-oo,-0.459] and
[0.91,3.733]
(D)
[-0.459,0.91] and
[3.733,oo)
(E) All real numbers](https://externalquestionsimg-a4fuc2b6e0gtdqge.z01.azurefd.net/external-question-images/images/images/ka/APCollegeCalculusBC/Applying%20derivatives%20to%20analyze%20functions/Calculator-active%20practice/Q-0.png)
The derivative of a function is given by .On which intervals is the graph of decreasing?Use a graphing calculator.Choose answer:(A) (B) and (C) and (D) and (E) All real numbers
Full solution
Q. The derivative of a function is given by .On which intervals is the graph of decreasing?Use a graphing calculator.Choose answer:(A) (B) and (C) and (D) and (E) All real numbers
- Identify Decreasing Intervals: To find where the graph of is decreasing, we need to look for intervals where is less than .
- Plot : Using a graphing calculator, we plot and look for intervals where the graph is below the -axis.
- Locate x-axis Intersections: The graph of crosses the x-axis at approximately and , which means the function changes from increasing to decreasing or vice versa at these points.
- Analyze Interval Behavior: Between and , the graph of is above the x-axis, indicating is increasing on this interval.
- Final Decreasing Intervals: Therefore, is decreasing on the intervals (- ext{\$\infty\)},\(1.]\) and [4.536, ext{\$\infty\)}).
