What are the minimum values?

Question

Find the equation which x solves if x is the location of the minimum value of g(x) = (1/x) sin (pi*x) on the interval [1, 2].

Im not sure if this will help: Hint: consider g(3/2) and g'(3/2).

how wod u solve for x without a graphing calc... and just a scientific calc?

Answer 1

g(x) is continuos in[1,2] and g(1)=g(2)=0
also the derivative exists in[1,2] so by the Rolle´s theorem there is a point where g´(x) =0
Also the function is negative

g´(x) =-1/x^2((pi*x*cos(pix)- sin( pi x)

pi*x*cospix -sin pix =0 which can be solved with a calculator
and gives x=1.43029665312