Question

25. Given the graph, answer the following questions: 2 L-00,-1) U(-1, 1)0 (1,2) UC2,2.5) U (2.5,00) 1 -1 At what domain points does the function appear to be: a) Differentiable? b) Continuous but t not differentiable? X=2,2.5 X=-1,1 c) Neither continuous nor differentiable?

Answer 1

Answer to the above question :

25. Based on the given graph,

(a) Differentiable domain of function :

( -
OX
, - 1) U ( -1, 1) U ( 1, 2) U ( 2 , 2.5) U ( 2.5,
OX
)

A differentiable function is a continuous function on its domain. The graph of a differentiable function must have a (non-vertical) tangent line at each point in its domain, be relatively "smooth" (but not necessarily mathematically smooth), and cannot contain any breaks, corners, or cusps.

(b)

Continuous but not differentiable :

x = 2 and x = 2.5

(c) Neither continuous nor differentiable :

x = -1 and x = 1

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