With today's technology and powerful computers, it is often tempting to think that the curve sketching process is not needed anymore. However, basing our conclusions on a sketch from a computer screen can be risky.

That is the case, for instance, with the function

f(x)=x⁴ - 408x³ + 3600x²

a) calculate f' and find the x-values of its extreme points

b) calculate f" and fid the x-values of its points of inflection (round to 2 decimals)

c) draw a sketch of the graph of f, that clearly shows extreme and inflection points

show all work please