Among the following statements, which are true and which are false? Every contin

Question

Among the following statements, which are true and which are false? Every continuous function n an open interval (a, b) assumes a maximum value. True False Every differentiate function is necessarily continuous. True False (c) Every continuous function ls necessarily differentiable. True False (d) Every continuous function which is somewhere positive and somewhere negative has a zero. True False (e) If for a differentiable function f(x), f'(x) = 0 for all real numbers x, then f(x) necessarily is a constant function. True False

Explanation / Answer

(a) In this question answer is true. Per the extreme value function.

(b) In this question answer is true.Every differentiable function is continuous but its vice versa is not true i.e every continuous function is not differentiable.

(c) In this question answer is false. Every continuous function is not differentiable

(d) In this question answer is true.

(e) In this question answer is true. If f '(x) = 0 for all x in (a,b) then f(x) is constant.

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