Use the function f(x)=2x3−3x2+7 to complete the exercises.f(−1)= f(1)= f(2)=

Answer 1

To evaluate the function \( f(x) = 2x^3 - 3x^2 + 7 \) at the specified values, we will substitute \(-1\), \(1\), and \(2\) into the function.

1. Calculating \( f(-1) \):

\[ f(-1) = 2(-1)^3 - 3(-1)^2 + 7 \] \[ = 2(-1) - 3(1) + 7 \] \[ = -2 - 3 + 7 \] \[ = -5 + 7 \] \[ = 2 \]

2. Calculating \( f(1) \):

\[ f(1) = 2(1)^3 - 3(1)^2 + 7 \] \[ = 2(1) - 3(1) + 7 \] \[ = 2 - 3 + 7 \] \[ = -1 + 7 \] \[ = 6 \]

3. Calculating \( f(2) \):

\[ f(2) = 2(2)^3 - 3(2)^2 + 7 \] \[ = 2(8) - 3(4) + 7 \] \[ = 16 - 12 + 7 \] \[ = 4 + 7 \] \[ = 11 \]

Putting it all together, we have:

\[ f(-1) = 2, \quad f(1) = 6, \quad f(2) = 11 \]