Question

What is dh/dx if h(x) = cπ, where c is a constant? Please show work. Will mark the best answer as brainliest.

Answer 1

Answer:

$h'(x)=0$

Step-by-step explanation:

By definition, the derivative of $f(x)$ is given by:

$\displaystyle \frac{dy}{dx}=f'(x)=\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$

Given $h(x)=c\pi$, $h(x+4)$ must also be $c\pi$. Therefore, we have:

$\displaystyle h'(x)=\lim_{h\rightarrow 0}\frac{c\pi - c\pi }{h},\\h'(x)=\lim_{h\rightarrow 0}\frac{0}{h}=\boxed{0}$

Note that the derivative of a constant is always zero since for $f(x)=c$, where $c$ is some constant, $f(x)=f(x+h)$ and we obtain $c-c$ in the numerator, yielding a final answer of zero.