Question

Graph x^4-3x^2+x. Identify the x-intercepts and the points where the local maximums and local minimums occur. Determine the intervals for which the function is increasing or decreasing. Round to the nearest hundredth, if necessary.

Answer 1

Functions, equations and tables can be represented using graphs

• The x-intercepts are: 0, 0.35 and 1.53
• The local maximum is at point (0.17, 0.08), and the local minimum is at point (1.13, -1.07)

The expression is given as:

$x^4-3x^2+x$

Rewrite the expression as a function

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

See attachment for the graph of the function.

The x-intercepts

This is the point where the graph cross the x-axis.

From the attached graph, the x-intercepts are: 0, 0.35 and 1.53

The local maximum

From the attached graph, the local maximum is at point (0.17, 0.08)

The local minimum

From the attached graph, the local minimum is at point (1.13, -1.07)

Intervals

• The graph increases at interval (-1.30, 0) and (1,13, infinity)
• The graph decreases at interval (- infinity, 1.30) and (0.35, 1.13)

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