Question

(1 point) Below is the graph of the derivative f'(x) of a function defined on the Interval (0,8). You can click on the graph to see a larger version in a separate window. n (A) For what values of x in (0,8) is f(x) increasing? Answer: Note: use interval notation to report your answer. Click on the link for details, but you can enter a single interval, a union of intervals, and if the function is never increasing, you can enter the empty set as (). (B) Find all values of x in (0,8) is where f(x) has a local minimum, and list them (separated by commas) in the box below. If there are no local minima, enter None. Local Minima:

Answer 1

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Shintion: Given: f(x) is defined on (0,8): asi f(x) is INCREASING. z f'(x) >0. → 5'lay is Positive 3 + (-5). Ans. to for having points of local muninum local maxinum? first, we have find the critical point for which f'(x) 20. => 2=3, *=5 two Citical points. are the a=3 x=5 Now, we find: at x= = 3 atx=5: filmey moves from NEGATIVE to Positive. > f(x) possesses local minimum at x = 3. (By the first Derivative Test) file) noves from Positive to NEGATIVE » f (x) possesses local maximum atx=5 (By the first Derivative Test).