Writing Lagrange's mean value theorem as f(b) − f(a) = (b − a) f′(c), a < c < b, the value of c, if f(x) = x(x − 1), a = 0, b = 1/2, isलैग्रान्ज के माध्यमान प्रमेय को f(b) − f(a) = (b − a) f′(c), a < c < b लिखने पर c का मान, यदि f(x) = x(x − 1), a = 0, b = 1/2 है, है
लैग्रान्ज के माध्यमान प्रमेय को f(b) − f(a) = (b − a) f′(c), a < c < b लिखने पर c का मान, यदि f(x) = x(x − 1), a = 0, b = 1/2 है, है
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Correct answer: (A) 1/41/4
Explanation
f(1/2) − f(0) = (1/2)(−1/2) = −1/4 and f′(c) = 2c − 1. So (1/2)(2c − 1) = −1/4, which gives 2c − 1 = −1/2 and c = 1/4.f(1/2) − f(0) = (1/2)(−1/2) = −1/4 और f′(c) = 2c − 1। अतः (1/2)(2c − 1) = −1/4, जिससे 2c − 1 = −1/2 और c = 1/4।