Question

question 2 · 1 point let $h(x)=f(x)g(x)$. if $f(x)=-3x^{2}+2x - 3$ and $g(x)=-3x^{2}+4x + 3$, what is $h(1)$? do not include \$h(1)=$\ in your answer. for example, if you found $h(1)=7$, you would enter 7. provide your answer below:

Explanation:

Step1: Find derivative of \(f(x)\)

$f'(x)=-6x + 2$

Step2: Find derivative of \(g(x)\)

$g'(x)=-6x + 4$

Step3: Use product - rule \((uv)^\prime = u^\prime v+uv^\prime\)

$h'(x)=f'(x)g(x)+f(x)g'(x)$

Step4: Substitute \(x = 1\)

$f(1)=-3+2 - 3=-4$, $g(1)=-3 + 4+3 = 4$, $f'(1)=-6 + 2=-4$, $g'(1)=-6 + 4=-2$
$h'(1)=(-4)\times4+(-4)\times(-2)=-16 + 8=-8$

Answer:

-8