Please answer all part of the question! This is Math(Real Analysis)

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 mayapply the squeeze theorem for limits of functions.) (c) Find f'(::) for 1: 71E 0. (In addition to the differentiation laws from (2135, youmay use the fact that the derivative ti sin(::) is 006(3).) (d) Using your computation in part (c), show that for any 6 > 0 there is a: with0<x<eandf{:c)<0.