Small question

[maxhk]

Hello everyone,

I have this small question :

"If $\displaystyle a, b, c$ are constants with $\displaystyle ab \neq 0$, show that the graph of $\displaystyle y = a \ \sin(bx+c)$ is always concave toward the x-axis."

What does concave toward the x-axis mean ? I don't understand what am I supposed to do ?

I understand what concave upward and concave downward are.

Thanks for your help!

 

[soroban]

Hello, maxhk!

What does concave toward the x-axis mean?

When the graph is above the $\displaystyle x$-axis, it is concave down.

When the graph is below the $\displaystyle x$-axis, it is concave up.

    |
    |        *
    |     *     *
    |   *         *
    |  *           *
    |
- - + * - - - - - - * - - - - - - * - -
    |
    |                *           *
    |                 *         *
    |                   *     *
    |                      *
    |

The "concave side" of the graph is always toward the $\displaystyle x$-axis.

 

[maxhk]

Ok, I see. Thanks Soroban!