Question

 

Let f(x)=x^2+x+13. What is the value of x for which the tangent line to the graph of y=f(x) is parallel to the x -axis?

x=

 

Answer 1

f'(x)=2x+1; the slope of the tangent line is zero when the tangent is horizontal (parallel to the x axis). f'(x) is the slope of the tangent and it's zero when 2x+1=0, when x=-1/2.