Chapter 12

Let \(f(1)=-2\) and \(f^{\prime}(x) \geq 4.2\) for \(1 \leq x \leq 6 .\) The possible value of \(f(6)\) lies in the interval : \(\quad\) [April 25, 2013] (a) \([15,19)\) (b) \((-\infty, 12)\) (c) \([12,15)\) (d) \([19, \infty)\)

If \(f(x)=3 x^{10}-7 x^{8}+5 x^{6}-21 x^{3}+3 x^{2}-7\), then \(\lim _{\alpha \rightarrow 0} \frac{f(1-\alpha)-f(1)}{\alpha^{3}+3 \alpha}\) is \(\quad\) [Online May 19, 2012] (a) \(-\frac{53}{3}\) (b) \(\frac{53}{3}\) (c) \(-\frac{55}{3}\) (d) \(\frac{55}{3}\)