f(x)= xsqrt((x^2)+16) is defined on the interval [-4,6]A. f(x) is concave down on the region ? B. f(x) is concave up on the region  ? C. The inflection point for this function is at x=?

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rcmath | High School Teacher | (Level 1) Associate Educator

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Denominator is always positive =>



f(x) concave down when f''(x)<0=>concave down on `[-4,0)`

f(x) concave up when f''(x)>0=> concave up on `(0,6]`

Thus point of inflection at x=0