The function f is graphed below. State the values that fulfill the following requirements.
If there are no such values, type DNE. If there are multiple discrete values, separate them with commas. If there are a whole interval of values that fulfill the requirement, use interval notation to give all of the values in the interval.
Type oo for ∞ and -oo for −∞. Also type U for ∪.
Where is f′=0 ? at x=
What are the values in the closed interval [−1.2,1.5] where f′ undefined? at x=
What are the critical values of f? at x=
Where is f′>0? ∀x in the interval
Where is f′<0 ? ∀x in the interval
Where does f have local minimums? What are these local minimum values? the relative minimum is which occurs at x=
Where does f have local maximums? the relative maximums occur at x=
Where does f have absolute minimums? What are these absolute minimum values? the absolute minimum is which occurs at x=
Where does f have absolute maximums? What are these absolute maximums values? the absolute maximum is which occurs at x=
Image developed from image at:
Strang, G., & Herman, E. (2016). Calculus Volume 1 (p. 404). Houston, TX: OpenStax.
Enter your answer as a list of values separated by commas: Example: -4, 3, 2 Enter each value as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity
Enter your answer as a list of values separated by commas: Example: -4, 3, 2 Enter each value as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity
Enter your answer as a list of values separated by commas: Example: -4, 3, 2 Enter each value as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity
Enter your answer using interval notation. Example: [2,5) Use U for union to combine intervals. Example: (-oo,2] U [4,oo) Enter each value as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for an empty set. Use oo to enter Infinity.
Enter your answer using interval notation. Example: [2,5) Use U for union to combine intervals. Example: (-oo,2] U [4,oo) Enter each value as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for an empty set. Use oo to enter Infinity.
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity
Enter your answer as a list of values separated by commas: Example: -4, 3, 2 Enter each value as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity
