If $$ f(x)=\frac{1}{3} x^{3}+c x^{2}+a x+5 $$ has alocal mintmum value at $$ x=1 $$. what is the value of $$ a $$ and $$ c $$ ?

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Wang Ortega · Accepted Answer

To have a local minimum at $$ x = 1 $$, the function $$ f(x) = \frac{1}{3} x^{3} + c x^{2} + a x + 5 $$ must satisfy: 1. $$ a = -1 - 2c $$ 2. $$ c > -1 $$ So, $$ a $$ and $$ c $$ are related by $$ a = -1 - 2c $$ with $$ c > -1 $$.

If \( f(x)=\frac{1}{3} x^{3}+c x^{2}+a x+5 \) has alocal mintmum value at \( x=1 \). what is the value of \( a \) and \( c \) ?

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If \( f(x)=\frac{1}{3} x^{3}+c x^{2}+a x+5 \) has alocal mintmum value at \( x=1 \). what is the value of \( a \) and \( c \) ?

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