let f(x)=x*e^x For what value of x is the slope of the line tangent to the graph of function f at [x,f(x)] equal to 1/2?
f(x)=xe^x,
f'(x)=e^x+xe^x=(x+1)e^x
For the tangent to have a slope of 1/2, equate
f'(x)=1/2 and solve for x:
(x+1)e^x=0.5
Solve by trial and error to be -0.315±