Question

question 18 · 1 point let h(x)=f(x)g(x). if f(x)= - 3x^{2}-4x + 2 and g(x)= - x^{2}+3x + 2, what is h(-1)? do not include \h(-1)=\ in your answer. for example, if you found h(-1)=20, you would enter 20. provide your answer below:

Explanation:

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

\(f'(x)=-6x - 4\)

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

\(g'(x)=-2x + 3\)

Step3: Use product - rule \((fg)'=f'g+fg'\)

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

Step4: Evaluate at \(x = - 1\)

\(f(-1)=-3+4 + 2=3\), \(g(-1)=-1 - 3+2=-2\), \(f'(-1)=6 - 4 = 2\), \(g'(-1)=2 + 3=5\)
\(h'(-1)=2\times(-2)+3\times5=-4 + 15 = 11\)

Answer:

11