14. [-/1 Points] DETAILS MY NOTES Find \( f^{\prime}(a) \). \( f(x)=4 x^{2}-5 x+3 \) \( f^{\prime}(a)=\square \)
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To find \( f^{\prime}(a) \), we first need to compute the derivative of the function \( f(x) = 4x^2 - 5x + 3 \). Using the power rule, the derivative \( f^{\prime}(x) \) is calculated as follows: \[ f^{\prime}(x) = \frac{d}{dx}(4x^2) - \frac{d}{dx}(5x) + \frac{d}{dx}(3) = 8x - 5. \] Now, to find \( f^{\prime}(a) \), simply substitute \( a \) into the derivative: \[ f^{\prime}(a) = 8a - 5. \] So, \( f^{\prime}(a) = 8a - 5 \). Now, you can use this expression to evaluate the derivative at any specific value of \( a \)! 🧐