Question

the following table lists the value of functions f and h, and their derivatives, f and h, for x = 4.

x	f(x)	h(x)	f(x)	h(x)

evaluate $\frac{d}{dx}2f(x)+2h(x)-3$ at x = 4.

Explanation:

Step1: Apply derivative rules

Use the sum - difference rule of derivatives $\frac{d}{dx}(u + v - w)=\frac{du}{dx}+\frac{dv}{dx}-\frac{dw}{dx}$ and the constant - multiple rule $\frac{d}{dx}(cf(x)) = c\frac{d}{dx}f(x)$. So, $\frac{d}{dx}[2f(x)+2h(x)-3]=2f'(x)+2h'(x)-0$.

Step2: Substitute $x = 4$

Substitute $x = 4$ into $2f'(x)+2h'(x)$. Given that $f'(4)=0$ and $h'(4)=6$, we have $2f'(4)+2h'(4)=2\times0 + 2\times6$.

Step3: Calculate the result

$2\times0+2\times6=0 + 12=12$.

Answer:

$12$