QuestionFebruary 3, 2026

Graph f(x)=x^4+3x^3-x^2-8x+2 Identify the x-intercepts and the points where the local maximums and local minimums occur. Determine the intervals for which the function is increasing or decreasing. Round to the nearest hundredth, if necessary. The x-intercept of the graph is xapprox square and a [Select] square The local maximum is [Select] ) and the local minimums are [ [Select] square square v square square v square square v The function is increasing when square and is decreasing when square v

Graph f(x)=x^4+3x^3-x^2-8x+2 Identify the x-intercepts and the points where the local maximums and local minimums occur. Determine the intervals for which the function is increasing or decreasing. Round to the nearest hundredth, if necessary. The x-intercept of the graph is xapprox square and a [Select] square The local maximum is [Select] ) and the local minimums are [ [Select] square square v square square v square square v The function is increasing when square and is decreasing when square v
Graph f(x)=x^4+3x^3-x^2-8x+2 Identify the x-intercepts and the points where the local maximums and local minimums occur. Determine the intervals for which the function is increasing or decreasing. Round to the nearest hundredth, if necessary. The x-intercept of the graph is xapprox square and a [Select] square The local maximum is [Select] ) and the local minimums are [ [Select] square square v square square v square square v The function is increasing when square and is decreasing when square v

Solution
4.6(312 votes)

Answer

The x-intercepts are approximately x \approx -3.62, -0.28, 1.40. The local maximum occurs at x \approx -2.25 with f(x) \approx 9.89, and the local minimum occurs at x \approx 0.25 with f(x) \approx -0.94. The function is increasing on the intervals (-\infty, -2.25) and (0.25, \infty), and decreasing on the intervals (-2.25, 0.25). Explanation 1. Find the x-intercepts Set f(x) = 0 and solve for x to find the x-intercepts. This may require numerical methods or graphing tools as it is a quartic equation. 2. Determine the critical points Find the derivative f'(x) and set it equal to zero to find critical points. Solve for x. 3. Classify critical points Use the second derivative test or the first derivative test to classify each critical point as a local maximum or minimum. 4. Determine intervals of increase or decrease Analyze the sign of f'(x) on intervals determined by the critical points to find where the function is increasing or decreasing.

Explanation

1. Find the x-intercepts<br /> Set $f(x) = 0$ and solve for $x$ to find the x-intercepts. This may require numerical methods or graphing tools as it is a quartic equation.<br />2. Determine the critical points<br /> Find the derivative $f'(x)$ and set it equal to zero to find critical points. Solve for $x$.<br />3. Classify critical points<br /> Use the second derivative test or the first derivative test to classify each critical point as a local maximum or minimum.<br />4. Determine intervals of increase or decrease<br /> Analyze the sign of $f'(x)$ on intervals determined by the critical points to find where the function is increasing or decreasing.
Click to rate:

Similar Questions