Select the limit that you would like to evaluate, and then move the slider to change the value of [math]h[/math]. Notice that:[br][list][*]the difference quotient (in blue) is equal to the slope of the secant line to [math]y=f\left(x\right)[/math] passing through [math]\left(c,f\left(c\right)\right)[/math] and [math]\left(c+h,f\left(c+h\right)\right)[/math], and [/*][*]the limit of the difference quotients (in red) is equal to the slope of the tangent line to [math]y=f\left(x\right)[/math] at [math]\left(c,f\left(c\right)\right)[/math].[/*][/list]Why is it clear that [math]f\left(x\right)[/math] is differentiable at [math]x=c[/math]?