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The function ff 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 ∪∪.
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- 2. Find all critical values, local extrema and the absolute maximum and absolute minimum values of f(x)= x(4-x)2 on the interval [0,5].find all values of x where the graph of g has a critical value. for each critical value, state whether the graph of g has a local maximum, local minimum, or neither. Justify your answer with a complete sentence.2. Give an example showing that, even if f0(c) = 0, it could happen that f(x) does not have a localmaximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?
- What is the minimum value of f(x) = x^2 - 8 ln x on the interval [1,5]Find the t coordinates of all critical points of the given function. Determine whether each critical point is a relative maximum, minimum, or neither by first applying the second derivative test, and if the test fails, by some other method. t=______(smaller value) t=______(larger value)A rectangular fence is to be constructed with one of its face adjacent to an existing wall. Given that the available materials for the fence are good for 24m, what dimensions will produce a maximum area for the fence? What is/are the function's critical point/s
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