Show that the function f(x) = x3 + 10x + 7 for x ∈ R is strictly increasing
f(x) = x3 + 10x + 7
∴ f′(x) = 3x2 + 10
3x2 ≥ 0 for all x ∈ R and 10 > 0
∴ f′(x) > 0 for all x ∈ R
Hence, f(x) is strictly increasing for all x ∈ R.
Concept: Increasing and Decreasing Functions
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