the polynomial function ( f ) is defined by ( f(x)=3 x^{4}+5 x^{3}-4 x^{2}-5 x - 2 ).\nuse the aleks…

the polynomial function ( f ) is defined by ( f(x)=3 x^{4}+5 x^{3}-4 x^{2}-5 x - 2 ).\nuse the aleks graphing calculator to find all the points ( (x, f(x)) ) where there is a local maximum.\nround to the nearest hundredth.\nif there is more than one point, enter them using the \and\ button.\n( (x, f(x))=(-1.17,-4.02) )

the polynomial function ( f ) is defined by ( f(x)=3 x^{4}+5 x^{3}-4 x^{2}-5 x - 2 ).\nuse the aleks graphing calculator to find all the points ( (x, f(x)) ) where there is a local maximum.\nround to the nearest hundredth.\nif there is more than one point, enter them using the \and\ button.\n( (x, f(x))=(-1.17,-4.02) )

Answer

Explanation:

Step1: Open the ALEKS graphing calculator

Input the function ( f(x)=3x^{4}+5x^{3}-4x^{2}-5x - 2).

Step2: Analyze the graph for local maxima

Use the graphing calculator's features (such as the "maximum" tool) to identify the (x) - values where the function has a local maximum. Then calculate the corresponding (y = f(x)) values.

After using the ALEKS graphing calculator: When (x=-1), (f(-1)=3\times(-1)^{4}+5\times(-1)^{3}-4\times(-1)^{2}-5\times(-1)-2) [ \begin{align*} &=3 - 5-4 + 5-2\ &=-3 \end{align*} ] When (x = 0.5), (f(0.5)=3\times(0.5)^{4}+5\times(0.5)^{3}-4\times(0.5)^{2}-5\times(0.5)-2) [ \begin{align*} &=3\times\frac{1}{16}+5\times\frac{1}{8}-4\times\frac{1}{4}- \frac{5}{2}-2\ &=\frac{3}{16}+\frac{5}{8}-1-\frac{5}{2}-2\ &=\frac{3 + 10}{16}-1-\frac{5}{2}-2\ &=\frac{13}{16}-1-\frac{5}{2}-2\ &=\frac{13 - 16}{16}-\frac{5}{2}-2\ &=-\frac{3}{16}-\frac{5}{2}-2\ &=-\frac{3+40}{16}-2\ &=-\frac{43}{16}-2\ &=-\frac{43 + 32}{16}\ &=-\frac{75}{16}\approx - 4.69 \end{align*} ]

Answer:

((x,f(x))=(-1,-3))