Describe the x-values at which the function is differentiable. y = |x2 – 25| g

can be rewritten as a piecewise function.since  we have (with quadratic inequalities)(the parabola is positive when it is not between    otherwise it is negative.the vertex is below the x-axis and it opens up with x-intercepts at x = -5, 5)differentiate both pieces with respect to x: the points are interests are at the places where the piecewise function breaks. those are places where we can have discontinuities in the derivative.see if the limits exist at  for the derivative.  compare left- and right-hand limits using pieces.comparing the pieces, we can easily see that at and at this means that the derivative is discontinuous at  ,  .it is not differentiable at those points. the slope changes too suddenly.so is differentiable on the interval