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March 29, 2017

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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?

  • Calculus - ,

    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±

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