If f(x) = x^4 - x^3 + 7x^2 + 14,then what is | vedclass

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(D) Given the function $f(x) = x^4 - x^3 + 7x^2 + 14$.To find the derivative $f^{\prime}(x)$,we apply the power rule $\frac{d}{dx}(x^n) = nx^{n-1}$:$f

Vedclass · Accepted Answer

$495$

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(D) Given the function $f(x) = x^4 - x^3 + 7x^2 + 14$.To find the derivative $f^{\prime}(x)$,we apply the power rule $\frac{d}{dx}(x^n) = nx^{n-1}$:$f^{\prime}(x) = \frac{d}{dx}(x^4) - \frac{d}{dx}(x^3) + 7 \cdot \frac{d}{dx}(x^2) + \frac{d}{dx}(14)$$f^{\prime}(x) = 4x^3 - 3x^2 + 7(2x) + 0$$f^{\prime}(x) = 4x^3 - 3x^2 + 14x$Now,substitute $x = 5$ into the derivative expression:$f^{\prime}(5) = 4(5)^3 - 3(5)^2 + 14(5)$$f^{\prime}(5) = 4(125) - 3(25) + 70$$f^{\prime}(5) = 500 - 75 + 70$$f^{\prime}(5) = 495$.

If $f(x) = x^4 - x^3 + 7x^2 + 14$,then what is the value of $f^{\prime}(5)$?

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