If the value of c prescribed in Rolle’s theorem for the function f(x) = 2x (x - 3)^n on the interval [0, 2√3] is 3/4,

Question

If the value of c prescribed in Rolle’s theorem for the function f(x) = 2x (x – 3)ⁿ on the interval [0, 2\(\sqrt{3}\)] is \(\frac{3}{4},\) write the value of n (a positive integer).

Answer 1

f(x) = 2x (x – 3)ⁿ

Differentiating the above-mentioned function with respect to ‘x’,

-n + 3 = 0

-n = -3

n = 3

Hence, the required value of ‘n’ is 3.