If g(x)=x4−3x3−x, the value of x such that g′(x)=12 is x = 2.67
The given function is:
[tex]g(x)=x^4-3x^3-x[/tex]
The derivative of the function g(x) is calculated below
[tex]g'(x)=4x^3-9x^2[/tex]
The question indicates that g'(x) = 12
This means that we are going to equate the derivative of g(x) gotten above to 12
[tex]4x^3-9x^2=12[/tex]
Solving the cubic equation above
The only real valid value of x is 2.67
Therefore, the value of x such that g′(x)=12 is x = 2.67
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