Posted by **Navroz** on Sunday, November 11, 2012 at 4:41pm.

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

- calculus -
**Jennifer**, Sunday, November 11, 2012 at 7:27pm
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

## Answer This Question

## Related Questions

- calculus - a function has a local maximum at x=-2 and x=6 and a local minimum at...
- 12th Calculus - use the derivative of the function y=f(x)to find the points at ...
- Math - When you're finding the sign of f' and f'' to find a local maximum/...
- Calulus - Consider the function y = 2x^3-3x^2+9x+5. 1. Find where the function ...
- Calculus - Find any absolute max/min and local max/min for the function f(x)=x^3...
- Calculus - Find any absolute maximum and minimum and local maximum and minimum ...
- Calculus - Consider f(x)=200+8x^3+x^4. find the intervals on which function is ...
- calc. - I'm having a lot of trouble with this problem: Sketch the graph and show...
- extrema - The function is given as y = 7x^3 - 8x^2 -16x +15 The max is at x = -4...
- PLEASE HELP!! DESPERATE!!! (MATH) - The derivative of a function is f'(x)=x(x+2...

More Related Questions