Question

y'=(4/5)(2cos(t)-sin(t))+(9/10)e^(-t/2)=0. How do I find the t, local max on Ti-89 calculator?

Answer 1

You don't. Just use the solve function to find where the derivative equals 0 or is non-existent (critical points). Then determine whether it's a maximum/minimum using the first/second derivative test.

@Idealist

Answer 2

I used a Tl-CAS calculator and in it you can use the solve function to type in the equation, then comma, then variable that you are solving for. In this case, the equation would be the derivative equal to 0 then comma, then whatever variable you were using.

Answer 3

I'm not sure if it's the same for the 89, but on the 83, when you graph something then press [2ND+TRACE] (or [CALC]), you get a menu.

Then, you'd select "4: maximum". You'll be brought back to the graph and you'll be asked for left/right bounds and a guess. When you have the desired interval bounds and a proper guess, press [ENTER]. Then you get the x- and y-coordinates of the maximum.

Surely this feature was retained in the 89 model, but I'm not familiar with the buttons you'd have to press to get what you're looking for.