Answered

At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Let g be the function given by g(x) = x^4-3^3-x. What are all values of x such that g'(x)=1/2

Sagot :

Answer:

The answer is "[tex]x= \frac{\sqrt[3]{3} }{2}[/tex]"

Step-by-step explanation:

Given:

[tex]\to g(x) = x^4-3^3-x \\\\\to g'(x) = \frac{1}{2}\\\\x=?[/tex]

Solve:

[tex]\to g(x) = x^4-3^3-x\\\\\to g(x) =x^4 -27-x \\\\\to g(x) =x^4 -x-27[/tex]

differentiate the above equation:

[tex]\to g'(x) = 4x^3- 1[/tex]

Given that:

[tex]\to g'(x)= \frac{1}{2}[/tex]

[tex]\to \frac{1}{2}= 4x^3 -1\\\\\to \frac{1}{2} +1= 4x^3 \\\\\to \frac{1+2}{2}= 4x^3 \\\\\to \frac{3}{2}= 4x^3 \\\\\to x^3 =\frac{3}{2 \times 4} \\\\\to x^3 =\frac{3}{8} \\\\ \to \bold{x= \frac{\sqrt[3]{3} }{2}}[/tex]

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.