Question

find the instantaneous rate of change for the function at the given value. f(x)=x^2 + 5x at x = 2
the instantaneous rate of change at x = 2 is

Explanation:

Step1: Find the derivative of the function

The derivative of $f(x)=x^{2}+5x$ using the power - rule. The power rule states that if $y = x^{n}$, then $y^\prime=nx^{n - 1}$. So, $f^\prime(x)=\frac{d}{dx}(x^{2})+\frac{d}{dx}(5x)=2x + 5$.

Step2: Evaluate the derivative at $x = 2$

Substitute $x = 2$ into $f^\prime(x)$. We get $f^\prime(2)=2\times2+5$.
$f^\prime(2)=4 + 5=9$.

Answer:

9