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(i) Let -1 le p le 1. Show that the equa...

(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 let`F'(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) = 0 ` for all `x ge 0`, then show that `f(x) = 0` for all `x ge 0.`

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