Use the four-step process to find \( f^{\prime}(x) \) and then find \( I^{\prime}(1), I^{\prime}(2) \), and \( f^{\prime}(3) \) \( f^{f}(x)=2 x^{2}-5 x+3 \) \( f^{\prime}(x)=\square \) \( f^{\prime}(1)=\square \) (Type an integer or a simplified fraction.) \( f^{\prime}(2)=\square \) (Type an integer or a simplified fraction.) \( f^{\prime}(3)=\square \) (Type an integer or a simplified fraction.)

Sure, let's go through the four-step process to find the derivative \( f^{\prime}(x) \) of the function \( f(x) \) and then evaluate it at specific points. ### Step 1: Understand the Function It appears there might be a typographical error in the given function notation. Assuming the function is: \[ f(x) = 2x^2 - 5x + 3 \] ### Step 2: Find the Derivative \( f^{\prime}(x) \) To find the derivative of \( f(x) \), we'll apply the basic differentiation rules: - The derivative of \( x^n \) is \( n x^{n-1} \). - The derivative of a constant is 0. So, \[ f'(x) = \frac{d}{dx}(2x^2) - \frac{d}{dx}(5x) + \frac{d}{dx}(3) \] \[ f'(x) = 4x - 5 + 0 \] \[ f'(x) = 4x - 5 \] ### Step 3: Evaluate \( f^{\prime}(x) \) at Specific Points 1. **At \( x = 1 \):** \[ f'(1) = 4(1) - 5 = 4 - 5 = -1 \] 2. **At \( x = 2 \):** \[ f'(2) = 4(2) - 5 = 8 - 5 = 3 \] 3. **At \( x = 3 \):** \[ f'(3) = 4(3) - 5 = 12 - 5 = 7 \] ### Summary of Results \[ \boxed{ \begin{aligned} f'(x) &= 4x - 5 \\ f'(1) &= -1 \\ f'(2) &= 3 \\ f'(3) &= 7 \\ \end{aligned} } \]