A.-B. --- C. --- For what interval of x is the graph of f concave upward? Select

Question

A.-B.

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C.

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For what interval of x is the graph of f concave upward? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type your answer in interval notation. Type an exact answer. Use a comma to separate answers as needed.) The graph is never concave upward. For what interval of x is the graph of f concave downward? Select the correct choice below and, if necessary, fill in the box to complete your choice. (Type your answer in interval notation. Type exact answer. Use a comma o separate answers as needed.) The graph is never concave downward.

Explanation / Answer

(d^2/dx^2(log(x^2-4 x+40)) = (-2 x^2+8 x+64)/(x^2-4 x+40)^2)

(-2 x^2+8 x+64 = -2(x+4)(x-8))

For concave upward f '' (x) > 0

For concave downward f '' (x) < 0

For inflection f '' (x) = 0 or f '' does not exist

Therefore

curve is concave upward for -4 < x < 8

curve is concave downward for x < -4 and x > 8

Inflection is at x= -4 and x = 8

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