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

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(C) Given,$f(x)=x^4-x^3+7x^2+14$. First,we find the first derivative $f^{\prime}(x)$ with respect to $x$: $f^{\prime}(x) = \frac{d}{dx}(x^4-x^3+7x^2+1

Vedclass · Accepted Answer

$284$

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(C) Given,$f(x)=x^4-x^3+7x^2+14$. First,we find the first derivative $f^{\prime}(x)$ with respect to $x$: $f^{\prime}(x) = \frac{d}{dx}(x^4-x^3+7x^2+14) = 4x^3-3x^2+14x$. Next,we find the second derivative $f^{\prime \prime}(x)$ by differentiating $f^{\prime}(x)$: $f^{\prime \prime}(x) = \frac{d}{dx}(4x^3-3x^2+14x) = 12x^2-6x+14$. Now,substitute $x=5$ into the expression for $f^{\prime \prime}(x)$: $f^{\prime \prime}(5) = 12(5)^2 - 6(5) + 14$. $f^{\prime \prime}(5) = 12(25) - 30 + 14$. $f^{\prime \prime}(5) = 300 - 30 + 14 = 284$. Thus,the value is $284$,which corresponds to option $C$.

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

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