Math  /  Calculus

Questionf(x)=x7x1/7f(x)=x-7 x^{1 / 7} (A) Find all critical values of ff. If there are no critical values, enter -1000 . If there are more than one, enter them separated by commas.
Critical value (s)=0,1(s)=0,1. (B) Use interval notation to indicate where f(x)f(x) is increasing.
Note: When using interval notation in WeBWorK, you use I for ,I\infty,-\mathrm{I} for -\infty, and U\mathbf{U} for the union symbol. If there are no values that satisfy the required condition, then enter the quotation marks.
Increasing: (,0)(1,)(-\infty, 0) \cup(1, \infty) (C) Use interval notation to indicate where f(x)f(x) is decreasing.
Decreasing: (0,1)(0,1) (D) Find the xx-coordinates of all local maxima of ff. If there are no local maxima, enter -1000 . If there are more than one, enter them separated by commas.
Local maxima at x=x= \square 0 (E) Find the xx-coordinates of all local minima of ff. If there are no local minima, enter -1000 . If there are more than one, enter them separated by commas.
Local minima at x=x= \square (F) Use interval notation to indicate where f(x)f(x) is concave up.
Concave up: (0,)(0, \infty) (G) Use interval notation to indicate where f(x)f(x) is concave down.
Concave down: (,0)(-\infty, 0) (H) Find all inflection points of ff. If there are no inflection points, enter -1000 . If there are more than one, enter them separated by commas. Inflection point(s) at x=x= \square

Studdy Solution
(A) Critical value(s): 0, 1 (B) Increasing: (,0)(1,)(-\infty, 0) \cup (1, \infty) (C) Decreasing: (0,1)(0, 1) (D) Local maxima at x=0x = 0 (E) Local minima at x=1x = 1 (F) Concave up: (0,)(0, \infty) (G) Concave down: (,0)(-\infty, 0) (H) Inflection point(s) at x=0x = 0

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