Q. 60 - Calculus

Question

In Exercises 59–62 use the derivative test in Theorem 7.6 to analyze the monotonicity of the given sequence.

$\left\{k^2-k\right\}$

Step-by-Step Solution

Answer

The given sequence is strictly increasing.

Step 1. Given Information.

The given sequence is $\left\{k^2-k\right\}.$

Step 2. Use the derivative test.

To analyze the monotonicity of the given sequence we will use the derivative test.

Let the function is $f\left(k\right)=k^2-k.$

According to the derivative test,

$f\text{'}\left(k\right)=2k-1$

Now, $f\text{'}\left(k\right)>0 \mathrm{for} \mathrm{all} k>0.$

Therefore, the given sequence is strictly increasing.