Question

Find the open intervals where the function f(x)=1/(x-8) is concave upward or concave downward. Find any inflection

Answer 1

hey mate here is your answer dear.
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To get the concavity, we need to take the second derivative of the function.

First, take f'(x) = 16/(x+2)^2 using the quotient rule

Next, take f''(x) = -32/(x+2)^3 using the quotient rule on the first derivative

Solving f''(x) = 0 would normally give the point of inflection, but in this case we'll get no solution, so we will inspect the critical value of x = -2.

Next, check a value smaller than x = -2 and a value larger than x = -2 to test for concavity (negative implies concave down).  

Let me know if this gets you going in the right direction!
hope it helps you dear