Question
Show that the function $f(x) = x^3 + 10x + 7$ for $x \in R$ is strictly increasing
✓
Answer
$f(x) = x^3 + 10x + 7$
$\therefore f′(x) = 3x^2 + 10$
$3x^2 \geq 0$ for all $x \in R$ and $10 > 0$
$\therefore f′(x) > 0$ for all $x \in R$
Hence, $f(x)$ is strictly increasing for all $x \in R$.
$\therefore f′(x) = 3x^2 + 10$
$3x^2 \geq 0$ for all $x \in R$ and $10 > 0$
$\therefore f′(x) > 0$ for all $x \in R$
Hence, $f(x)$ is strictly increasing for all $x \in R$.
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