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question 1

let ( f(x) = 2x^3 - 6x^2 + 4x + 7 ).

evaluate ( f(4) ). if necessary, round accurate to two decimal places. if this value is undefi

Explanation:

Step1: Substitute \( x = - 4 \) into \( f(x) \)

We have the function \( f(x)=2x^{3}-6x^{2}+4x + 7 \). When \( x=-4 \), we substitute \( x=-4 \) into each term:

• For the term \( 2x^{3} \): \( 2\times(-4)^{3}=2\times(-64)=- 128 \)
• For the term \( -6x^{2} \): \( -6\times(-4)^{2}=-6\times16=-96 \)
• For the term \( 4x \): \( 4\times(-4)=-16 \)
• The constant term is \( 7 \)

Step2: Sum up all the terms

Now we sum up these results: \( f(-4)=2\times(-4)^{3}-6\times(-4)^{2}+4\times(-4)+7=-128-96 - 16+7 \)
First, calculate \( -128-96=-224 \), then \( -224-16=-240 \), and finally \( -240 + 7=-233 \)

Answer:

\( -233 \)