Question

Use a table to graph (the equation in the photo). Then estimate the x-coordinates at which relative maxima and relative minima occur.

Answer 1

Given,

$f(x)=-2x^3+12x^2-8x$

Construct a table containing two columns, one representing the value of x and the other representing the value of y = f(x).

$\begin{gathered} x,y \\ 0,\text{ 0} \\ 1,\text{ 2} \\ -1,22 \\ \text{.} \\ \text{.} \\ \text{.} \end{gathered}$

From the graph, the relative minima are at (0.367,-1.419) and the relative maxima are at (3.633,33.419).

While creating the table, we will try to reach as close to these points by the hit and trial method.

As a result, the relative minima is at x = 0.367 and the relative maxima is at x= 3.633.