Question

find the interval of the equation which function f is concave up or down locate inflection point f(x)=(x+2)^3​

Answer 1

We need to compute and study the sign of the second derivative:

$f(x) = (x+2)^3 \implies f'(x) = 3(x+2)^2 \implies f''(x) = 6(x+2)$

So, we have

$f''(x)>0 \iff 6(x+2)>0 \iff x+2>0 \iff x>-2$

So, this function is concave down before -2 (the second derivative is negative), it changes at x=-2 (inflection point), and it's concave up after -2 ( the second derivative is positive)