For the following questions, choose the correct answers from the codes (a), (b), (c) and (d) def...

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For the following questions, choose the correct answers from the codes (a), (b), (c) and (d) defined as follows.
(a) Statement I is true, Statement II is also true, Statement II is the correct explanation of Statement I
(b) Statement I is true, Statement II is also true, Statement II is not the correct explanation of Statement I
(c) Statement I is true, Statement II is false
(d) Statement I is false, Statement II is true
Let \( f(x) \) be a twice differentiable function in \( [a, b] \), given that \( f(x) \) and \( f^{\prime \prime}(x) \) has same sign in \( [a, b] \).
Statement I \( f^{\prime}(x)=0 \) has at the most one real root in \( [a, b] \). Statement II An increasing function can intersect the \( X \)-axis at the most once.
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