### Home > CALC > Chapter Ch3 > Lesson 3.4.3 > Problem 3-174

3-174.

Sketch the graph of *f*(*x*) = *x*(*x* − 1), and use this graph to sketch the graph of the slope function, *f *′(*x*). Homework Help ✎

*f*(*x*) is a parabola,so *f* '(*x*) will be linear.

Notice the negative slope when *x* < 0.5. This means the graph of *f* '(*x*) will have negative values on this domain.

Notice the positive slope when *x* > 0.5. This means the graph of *f* '(*x*) will have positive values on this domain.

Notice that *x* = 0.5 is the *x*-value of the local minimum. This means the graph of *f* '(*x*) will have a root at *x* = 0.5.

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