(i) Let -1 le p le 1. Show that the equation 4x^(3) - 3x - p = 0 has a unique root in the interval [1/2, 1] and identiify it. (ii) Let f(x), x ge 0, be a nonnegative continuous function , and letF'(x) = f(x)= (4a-3)(x+log5)+2(a-7)cotx/2 sin^(2) x/2, x ge 0. If for some c gt 0, f(x) ltcF(x)for all x ge 0, then show that f(x) = 0for all x ge 0, then show that f(x) = 0 for all x ge 0.

(i) Let -1 le p le 1. Show that the equation 4x^(3) - 3x - p = 0 has a

1.	(i) Let -1 le p le 1. Show that the equation 4x^(3) - 3x - p = 0 has a unique root in the interval [1/2, 1] and identiify it. (ii) Let f(x), x ge 0, be a nonnegative continuous function , and letF'(x) = f(x)= (4a-3)(x+log5)+2(a-7)cotx/2 sin^(2) x/2, x ge 0. If for some c gt 0, f(x) ltcF(x)for all x ge 0, then show that f(x) = 0for all x ge 0, then show that f(x) = 0 for all x ge 0.
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