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f(x) = x - 7x 1/7 Find all critical values of f. If there are no critical values

ID: 3194327 • Letter: F

Question

f(x) = x - 7x 1/7 Find all critical values of f. If there are no critical values, enter -1000. If there are more than one, enter them separated by commas. Critical value(s) = Use interval notation to indicate where f (x) is increasing. Note: When using interval notation in WeBWorK, you use I for infinity, -I for -infinity, and U for the union symbol. If there are no values that satisfy the required condition, then enter "{}" without the quotation marks. Increasing: Use interval notation to indicate where f (x) is decreasing. Decreasing: Find the x-coordinates of all local maxima of f. If there are no local maxima, enter -1000. If there are more than one, enter them separated by commas. Local maxima at x = Find the x-coordinates of all local minima of f. If there are no local minima, enter -1000. If there are more than one, enter them separated by commas. Local minima at x = Use interval notation to indicate where f (x ) is concave up. Concave up: Use interval notation to indicate where f (x) is concave down. Concave down: Find all inflection points of f. If there are no inflection points, enter -1000. If there are more than one, enter them separated by commas. Inflection point(s) at x =

Explanation / Answer

f(x) = x- 7x^1/7


f'(x) = 0


1 - 7 *1/7 x^(1/7 -1) = 0

=> x^(-6/7) = 1


=> critical point ,x = 1