# TI-BASIC:Fmax

From Learn @ Cemetech

Jump to navigationJump to search**Command Summary**

Calculates the local maximum of a function.

**Command Syntax**

fMax(*f*(*var*),*var*,*lo*,*hi*[,*tol*])

**Menu Location**

While editing a program, press:

- MATH to open the Math menu
- 7 or use arrow keys to select

TI-83/84/+/SE

1 byte

fMax(*f*(*var*),*var*,*lo*,*hi*[,*tol*]) finds the value of *var* between *lo* and *hi* at which the maximum of *f*(*var*) occurs. *tol* controls the accuracy of the maximum value computed. The default value of *tol* is 10^{-5}.

fMax( only works for real numbers and expressions. Brent's method for optimization is used for approximating the maximum value.

fMax(sin(X)cos(X),X,0,3) .7853995667

Keep in mind that the result is the value of *var*, and not the value of *f(var)*. In this example, .7853995667 is not the highest possible value of sin(X)cos(X), but rather the X-value at which sin(X)cos(X) is the highest.

# Error Conditions

**ERR:BOUND**is thrown if the lower bound is greater than the upper bound.**ERR:DOMAIN**is thrown if*tol*is 0.**ERR:TOL NOT MET**is thrown if the tolerance is too small for this specific function.