Answer
The maximum slope of the tangent to the function f(x) = -x^3 + 4x - 2 is 4
Explanation
Given function:
[tex]f(x)=-x^3+4x-2[/tex]What to find:
The maximum slope of the tangent to the given function.
Step-by-step solution:
The slope of the tangent for the equation is given by the derivative of the function, which is:
[tex]\begin{gathered} f(x)=-x^3+4x-2 \\ \\ f^{\prime}(x)=-3x^2+4 \\ \\ f^{\prime}^{\prime}(x)-6x\Rightarrow x=0 \\ \\ Putting\text{ }x=0\text{ }into\text{ }f(x) \\ \\ -3x^2+4 \\ \\ \Rightarrow f^{\prime}(0)=-3(0)+4 \\ \\ f^{\prime}(0)=4 \end{gathered}[/tex]Therefore, the maximum slope of the tangent to the given function is 4
