Question:
show that function f(x) = x*3 - 3x*2 6x - 100 is increasing on R
Answer:
Given, function f(x) = x3 - 3x2 + 6x - 100
Differentiate w.r.t. x, we get
df(x)/dx = 3x2 - 6x + 6
=> df(x)/dx = 3x2 - 6x + 3 + 3
=> df(x)/dx = 3(x2 - 2x + 1) + 3
=> df(x)/dx = 3(x -1)2 + 3 > 0
Since df(x)/dx > 0
Hence, f(x) is always increasing on R
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