Let f(x)= array cc e^ x , & 0 x 1 2-e^ x-1 , & 1 and g(x)= _ 0 ^ x f(t) d t, x [1,3] then…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Let \[f(x)=\left\{\begin{array}{cc}
e^{x}, & 0 \leq x \leq 1 \\
2-e^{x-1}, & 1and \(g(x)=\int_{0}^{x} f(t) d t, x \in[1,3]\) then g(x) has
- local maxima at x = 1 + ln 2 and local minima at
x = e - local maxima at x = 1 and local minima at x = 2
- no local maxima
- no local minima
Answer
(B) local maxima at x = 1 and local minima at x = 2
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