problem solving derivative

Hi, I want to find the peak value (extrema) of my distribution which is:

y = (ka/landa)*((x/landa)^(ka-1))* (2^(-(x/landa)^ka));

so first I calculate the first derivation based on different values of landa and ka

z= diff(y);

and then I solve this equation, but for some values of landa and ka, I dont get any answer(explicit solution could not be found), for example for ka= 0.17 and landa=0.13. When I calculate the second derivation is also the same. Could you please tell me if there is another way or where is my mistake? tanx Sasi

Answer 1

[Friedrich]

Hi,

for ka = 0.17 and landa = 0.13 there is no extrema. You can plot the derivative to see that:

syms x
ka= 0.17
landa=0.13
y = (ka/landa)*((x/landa)^(ka-1))* (2^(-(x/landa)^ka));
z = diff(y)
steps = -1:0.1:1;
g = matlabFunction(z)
plot(steps,g(steps))

0 is a asymptote here. So you will never reach 0. Thats why you get this message.