Question 3 of 24 Resources Al Tutor (C) Submit Answer Find the critical number(s) of the following function. \[ f(x)=x^{3}+6 x^{2}+12 x+5 \] (Give your answer in the form of a comma-separated list. Express numbers in exact form. Use symbolic notation and fractions where needed.) critical number(s): \( \square \) Use the First Derivative Test to find any local extrema of \( f \). (Give your answer in the form of a comma-separated list. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if there are no local maximums or minimums.) local maximum value(s): \( \square \) local minimum value(s): \( \square \)
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The derivative is: \[ f'(x) = 3x^2 + 12x + 12 \] Show more…
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Locate the critical points of the following function. Then use the Second Derivative Test to determine whether they correspond to local maxima, local minima, or neither. What is(are) the critical point(s) of f? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The critical point(s) is(are) x = (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) B. There are no critical points for f. What is/are the local minimum/minima of f? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The local minimum/minima of f is/are at x = (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) B. There is no local minimum of f. What is/are the local maximum/maxima of f? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The local maximum/maxima of f is/are at x = (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) B. There is no local maximum of f.
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Consider the following function f(x) = 2x^3 - 15x^2 + 36x - 2. Find the derivative. f'(x) = 6x^2 - 30x + 36. Find any critical numbers of the function. (Enter your answer as a comma-separated list. If any answer does not exist, enter DNE) x = 2, 3. Find the interval(s) on which f is increasing. (Enter your answer using interval notation.) (-∞, 2) ∪ (3, ∞). Find the interval(s) on which f is decreasing. (Enter your answer using interval notation.) (2, 3). Find the local minimum and maximum value of f. Local minimum value: 25. Local maximum value: 26.
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