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Show that the function f(x) = x3 + 10x + 7 for x ∈ R is strictly increasing - Mathematics and Statistics

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Sum

Show that the function f(x) = x3 + 10x + 7 for x ∈ R is strictly increasing

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Solution

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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