Question

1. use technology to graph ( f ( x ) = 0.7 x ^ { 4 } - 3 x ^ { 2 } + 5 x ).

part a. identify the ( x )-intercepts and the points where the local maxima and local minima occur.
from least to greatest, ( x )-intercepts
are
①
the local maximum is
②
the local minimums are
③

Explanation:

Step1: Identify x - intercepts

The x - intercepts are the values of \(x\) for which \(y = f(x)=0\). Looking at the given options for x - intercepts: \(x\approx - 1.15,x = 0,x\approx1.64,x\approx3.79\)

Step2: Identify local maximum

The local maximum is a point where the function changes from increasing to decreasing. From the given points \((0.87,2.78)\) is the local maximum.

Step3: Identify local minima

The local minima are points where the function changes from decreasing to increasing. The points \((0.07,1.12)\) and \((3,0.17)\) are local minima.

Answer:

1. \(x\approx - 1.15,x = 0,x\approx1.64,x\approx3.79\)
2. \((0.87,2.78)\)
3. \((0.07,1.12)\) and \((3,0.17)\)