Question

if (f(x)=\frac{1}{19}x^{19}), what is (f(1.05)?)

Explanation:

Step1: Apply power - rule for differentiation

The power - rule states that if $f(x)=ax^n$, then $f^\prime(x)=nax^{n - 1}$. Here, $a=\frac{1}{19}$ and $n = 19$. So, $f^\prime(x)=19\times\frac{1}{19}x^{19 - 1}=x^{18}$.

Step2: Evaluate $f^\prime(x)$ at $x = 1.05$

Substitute $x = 1.05$ into $f^\prime(x)$. So, $f^\prime(1.05)=(1.05)^{18}$.
Using a calculator, $(1.05)^{18}\approx2.4066$.

Answer:

$2.4066$