Question

let f be the function given by f(x)=3 sin x + 8e^x. what is the value of f(0)?

Explanation:

Step1: Differentiate term - by - term

Use derivative rules. The derivative of $\sin x$ is $\cos x$ and the derivative of $e^{x}$ is $e^{x}$. So, if $f(x)=3\sin x + 8e^{x}$, then $f'(x)=3\cos x+8e^{x}$.

Step2: Evaluate at $x = 0$

Substitute $x = 0$ into $f'(x)$. We know that $\cos(0)=1$ and $e^{0}=1$. So $f'(0)=3\times\cos(0)+8\times e^{0}=3\times1 + 8\times1$.

Step3: Calculate the result

$f'(0)=3 + 8=11$.

Answer:

D. 11