Question

a function has a local maximum at x=-2 and x=6 and a local minimum at x=1. how do u find the concavity of this function and point of inflection??
***the only given info is the max and min points

Answer 1

Imagine what is happening from (-infinity < x < infinity)

1). from -infinity to x = -2, the graph is going up, then reaches a maximum at x = -2
2). From x = -2 to x = 1, the graph is going down to the minimum at x = 1
3). From x = 1 to x = 6, the graph goes up again to its maximum at x = 6
4). From x = 6 to +infinity, the graph must go down again.

So the graph will kind of look like two hills with one inflection point between x = -2 and x = 1, and another between x = 1 and x = 6

The function is concave down from - infinity to inflection point 1; concave up from inflection point1 to inflection point 2, and concave down from inflection point 2 to infinity.

The inflection points are found by solving the equation f''(x) = 0