i expect your supposed to follow through on a full product rule etc but there are other ways to look at this.
first compute #f(1) = 4(-7)(-2) = 56#
then compute #delta f = f(1+h) - f(1)# where # h# is a small displacement such that # h \to 0#
#delta f = f(1+h) - f(1) =(4+h)(-7+h)(-2+h) - f(1)#
# = (4+h) (14 -9h +h^2)- f(1)#
the neat thing is we only need look at constant and #h^1# terms, ignoring higher order # h^2, h^3 ,...# terms, because #h \to 0# so those higher order terms are orders of magnitude smaller.
so
#delta f = (4+h) (14 -9h +h^2)- f(1)#
# = 56 + h(-36+14) - 56 + \mathcal{O} (h^2)#
# = -22h + \mathcal{O} (h^2) #
now for # h > 0#, we have #delta f < 0#. for #h < 0#, we have #delta f > 0# so this function is decreasing as it passes through #x = 1#
moreover, the actual slope at #x = 1# should be given by #lim_{h \to 0} [(delta f)/(h) ]_{x=1}= -22 + \mathcal{O} (h) = -22#
