Thread: root of equation

hello how would i show that the equation has one real root..

am not sure what to do with the function

You want the zeros of , . Observe by differentiation that f is strictly increasing. Therefore if f has at most one root, since if a<b were two distinct roots we could chuse a<c<b, and 0=f(a)<f(c)<f(b)=0, a contradiction. To see that one root exists, evaluate f near zero to get a negative value and then above 4 to get a positive value and use the IVT.

Hello, sigma1!

How about a graphing approach?

How would i show that the equation has one real root?

Graph the functions: . . and note their intersection(s), if any.

Code:

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      * |
       4o
        | *                     *
        |   *            *
        |     *     *
        |       ◊
        |    *    *
    - - + -o- - - - o - - - - - - - - - -
        | *1        4  *
        |                 *
        |*
        |