Question

1. Explain why the following statements are false by giving a counterexample and Change the conditions...

1.

  • Explain why the following statements are false by giving a counterexample and
  • Change the conditions of the statement so that it is correct

(a) If f(x) is continuous on (a, b] and (b, c), then f(x) is continuous at b.

(b) If the left-handed and right-handed derivatives of f(x) are the same at x=c , then f'(c) exists.

(c) If f'(x) > 0 for every x, then f(x) is decreasing.

(d) If f(x) is not differentiable at x=c, then f(x) is not continuous at x=c.

(e) If f(0)= -1 and f(1)= 1, then there is some number c between 0 and 1 so that f(c)= 0.

Math   Calculus   
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