Question

h(x)=2f(x)-3g(x)+5
h(4)=square
x f(x) g(x) f(x) g(x)
4 - 4 13 0 8

Explanation:

Step1: Differentiate $H(x)$ using sum - difference rule

By the sum - difference rule of differentiation $(u - v+w)'=u'-v'+w'$, if $H(x)=2f(x)-3g(x) + 5$, then $H'(x)=2f'(x)-3g'(x)$.

Step2: Substitute $x = 4$

We need to find $H'(4)$. Substitute $x = 4$ into $H'(x)$. So $H'(4)=2f'(4)-3g'(4)$.

Step3: Use given values

From the table, when $x = 4$, $f'(4)=0$ and $g'(4)=8$. Then $H'(4)=2\times0-3\times8$.

Step4: Calculate the result

$H'(4)=0 - 24=-24$.

Answer:

$-24$