### Home > CALC > Chapter 4 > Lesson 4.1.3 > Problem 4-37

Sketch a graph of *f*(*x*) = *x*^{3} − 2*x*^{2} . At what point(s) will the line tangent to* f*(*x*) be parallel to the secant line through (0, *f*(0)) and (2, *f*(2))? Homework Help ✎

Calculate the slope of the secant between (0, *f*(0)) and (2, *f*(2)).

We want to know where the slope of the tangent is the same as the slope of the secant. Recall that the slope of the tangent is also

known as *f* '(*x*), find where *f* '(*x*) = 0.

The slope of the tangent = the slope of the secant at coordintate points ( ________, _________ ) and ( ________, _________ ). You must analytically compute the exact coordintaes, but note that the slope of tangents lines is 0 at the local maximum and local minimum.

Use the eTool below to examine the graph.

Click the link at right for the full version of the eTool: Calc 4-37 HW eTool