if f is the function given by $f(x)=\frac{4}{x}+5x - 1$, then $f(2)=$\n(a) 4\n(b) 6\n(c) 7\n(d) 11
if f is the function given by $f(x)=\frac{4}{x}+5x - 1$, then $f(2)=$\n(a) 4\n(b) 6\n(c) 7\n(d) 11
Answer
Explanation:
Step1: Rewrite the function
Rewrite $f(x)=\frac{4}{x}+5x - 1$ as $f(x)=4x^{-1}+5x - 1$.
Step2: Differentiate the function
Using the power - rule $\frac{d}{dx}(x^n)=nx^{n - 1}$, we have $f^\prime(x)=4\times(-1)x^{-2}+5=- \frac{4}{x^{2}}+5$.
Step3: Evaluate $f^\prime(2)$
Substitute $x = 2$ into $f^\prime(x)$: $f^\prime(2)=-\frac{4}{2^{2}}+5$. First, calculate $\frac{4}{2^{2}}=\frac{4}{4} = 1$. Then $f^\prime(2)=-1 + 5=4$.
Answer:
A. 4