Answered

Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Determine whether f(x) =1/2x2-x-9 has a maximum or a minimum value and find that value.

Determine Whether Fx 12x2x9 Has A Maximum Or A Minimum Value And Find That Value class=

Sagot :

Given:

[tex]f(x)=\frac{1}{2}x^2-x-9[/tex]

Differentiate with respect to 'x'

[tex]\begin{gathered} f^{\prime}(x)=\frac{1}{2}(2x)-1 \\ f^{\prime}(x)=x-1 \end{gathered}[/tex]

Let f'(x)=0

[tex]\begin{gathered} x-1=0 \\ x=1 \end{gathered}[/tex][tex]\begin{gathered} f^{\doubleprime}(x)=1 \\ f^{\doubleprime}(x)>0 \end{gathered}[/tex]

Therefore, the function f(x) is minimum

[tex]\begin{gathered} f(1)=\frac{1}{2}(1)^2-1-9 \\ f(1)=\frac{1}{2}-1-9 \\ f(1)=\frac{1-2-18}{2} \\ f(1)=-\frac{19}{2} \\ f(1)=-9.5 \end{gathered}[/tex][tex]\text{Therefore, the minimum point is (1,-9.5)}[/tex]

Option d is the final answer.

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.