Answered

Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable 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 platform. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.