Identify whether the claim is accurate or not. If it's accurate, describe why. If it's untrue, explain why or provide an illustration that refutes it. Derivatives exist for all continuous functions.

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Identify whether the claim is accurate or not. If it&#039;s accurate, describe why. If it&#039;s untrue, explain why or provide an illustration that refutes it. Derivatives exist for all continuous functions.

svartmaleJ · Accepted Answer

Step 1&amp;nbsp;Given,&amp;nbsp;Statement: Derivatives exist for all continuous functions.Step 2&amp;nbsp;All continuous functions have derivatives, but this claim is untrue.Example: The absolute value function abs x is continuous everywhere but it is not differentiable at x = 0&amp;nbsp;Since,&amp;nbsp;f(x)=−x,−∞≤x≤0&amp;nbsp;=x,0≤x≤∞&amp;nbsp;Left hand derivative at x = 0 is, -1 and right hand derivative at x = 0 is 1.&amp;nbsp;Hence the absolute value function is continuous but not differentiable at x = 0.

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.All continuous functions have derivatives.

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