Consider the function f(.1:)={:1 +1: sin(1/.12) :163- (a) Show that ﬁx) is minimised at 0. (b) Use the deﬁnition of derivatiw (as a limit) to show that f’(0) = 0. (You may

apply the squeeze theorem for limits of functions.) (c) Find f'(::) for 1: 71E 0. (In addition to the differentiation laws from (2135, you

may use the fact that the derivative ti sin(::) is 006(3).) (d) Using your computation in part (c), show that for any 6 gt; 0 there is a: with

0lt;xlt;eandf{:c)lt;0. Math