Question

What is the maximum slope of the tangent to to the function f(x) = -x^3 + 4x - 2?

Answer 1

The maximum slope of the tangent to the function f(x) = -x^3 + 4x - 2 is 4

Step-by-step explanation

Given function:

`f(x)=-x^3+4x-2`

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:

`\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}`

Therefore, the maximum slope of the tangent to the given function is 4