Question

If f(x) = {(e^x, 0 ≤ x ≤ 1), (2 - e^{x - 1}, 1 < x ≤ 2), (x - e, 2 < x ≤ 3) and g(x) = ∫f(t)dt for t ∈ [0, x], x ∈ [1, 3] then g(x) has

(a) local maxima at x = 1 + log2

(b) local maxima at x = 1 and local minima at x = 2

(c) local maxima at x = e

(d) local minima at x = e

Answer 1

Correct option (a, d)

Explanation:

Thus g (x) has a local maximum at x = 1 + log2 and a local minima at x = e.