Find the intervals on which the graph of f is concave upward, the intervals on w

ID: 3343987 • Letter: F

Question

Find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the inflection points.

f(x)=x^14+2x^2

For what interval(s) of x is the graph of f concave upward? _______(Type answer INTERVAL NOTATION, Exact Answer)

For what interval(s) of x is the graph of f concave downward?_______(Type answer INTERVAL NOTATION, Exact Answer)

Determine the x coordinates of any inflection points of the graph of f(x).______ (Type answer INTERVAL NOTATION, Exact Answer)

f(x)=x^14+2x^2 f'(x) = 14x^13 + 4x f''(x) = 14*13x^12 + 4 f'(x) = 0 we get x = 0, x = [-2/7]^(1/12) f''(0) = 4 > 0 so, concave up

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