Question

let f and g be differentiable functions such that f(0) = 3 and g(0) = 7. if h(x)=3f(x)-2g(x)-5cos x - 3, what is the value of h(0)?
a -8
b -5
c 1
d 28

Explanation:

Step1: Differentiate h(x)

Using sum - difference and constant - multiple rules of differentiation, if $h(x)=3f(x)-2g(x)-5\cos x - 3$, then $h'(x)=3f'(x)-2g'(x)+5\sin x$.

Step2: Substitute x = 0

Substitute $x = 0$ into $h'(x)$. We know that $f'(0) = 3$, $g'(0)=7$, and $\sin(0)=0$. So $h'(0)=3f'(0)-2g'(0)+5\sin(0)$.

Step3: Calculate the value

$h'(0)=3\times3-2\times7 + 5\times0=9 - 14+0=-5$.

Answer:

B. -5