I'm trying to derive the following two inequalities for the exponential function, where x,y,z in R, t>0 and a>1 |y-z|e^{-{(y-z)^2}/{2at}}leq C_at^{1}/{2}e^{-{(y-z)^2}/{4at}}, t^{-{1}/{a}}|y-z|^{1+{2}/{a}}e^{-{(y-z)^2}/{2at}}leq C_at^{1}/{2}e^{-{(y-z)^2}/{4at}}, with some constant C_a>0 I tried to derive it by using derivatives but it didn't work for the purpose.

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function
$f(x,y)=x^3-6xy+8y^3$

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