Suppose that f(x) = 6x2 - 6x5. Find all critical numbers of f. If there are no c

Question

Suppose that f(x) = 6x2 - 6x5. Find all critical numbers of f. If there are no critical numbers, enter 'NONE'. Critical numbers = Use interval notation to indicate where f (x) is increasing. Note: Use 'INF' for infinity, '-INF' for -infinity, and use 'U' for the union symbol. 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 'NONE'. X values of local maxima = Find the x-coordinates of all local minima of f. Note: If there are no local minima, enter 'NONE'. X values of local minima = 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: List the x values of all inflection points of f. If there are no inflection points, enter 'NONE'. X values of inflection points = Find all horizontal asymptotes of f. If there are no horizontal asymptotes, enter 'NONE'. Horizontal asymptotes y = Find all vertical asymptotes of f. If there are no vertical asymptotes, enter 'NONE'. Vertical asymptotes x =

Explanation / Answer

f'(x) = 6*6x^5 - 6*5 x^4 = 0

=> 6x^4 {6x - 5 } = 0

=> x= 0, 5/6

to find inflection point ,f"(x) = 0

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