hw9 the derivative as a function (targets l6, d1, d2; §3.2)\nscore: 8/9 answered: 8/9\nquestion 9\nselect…

hw9 the derivative as a function (targets l6, d1, d2; §3.2)\nscore: 8/9 answered: 8/9\nquestion 9\nselect all the points at which the graph above is not differentiable\n□ - 4\n□ - 3\n□ - 2\n□ - 1\n□ 0\n□ 1\n□ 2\n□ 3\n□ 4

hw9 the derivative as a function (targets l6, d1, d2; §3.2)\nscore: 8/9 answered: 8/9\nquestion 9\nselect all the points at which the graph above is not differentiable\n□ - 4\n□ - 3\n□ - 2\n□ - 1\n□ 0\n□ 1\n□ 2\n□ 3\n□ 4

Answer

Explanation:

Step1: Recall non - differentiability conditions

A function is not differentiable at a point if there is a sharp corner, a cusp, a vertical tangent, or a discontinuity at that point.

Step2: Analyze the graph

  • At (x=-2), there is a sharp corner. The slope of the left - hand side and the right - hand side of the function at (x = - 2) are different, so the derivative does not exist.
  • At (x = 0), there is a discontinuity (a hole in the graph). Since the function is not continuous at (x=0), it is not differentiable at (x = 0).
  • At (x=3), there is a vertical tangent. As the slope of the tangent line approaches infinity at (x = 3), the function is not differentiable at this point.

Answer:

-2, 0, 3