Problem 40
A function \(f(x)\) is given. Find the critical points of \(f\) and use the Second Derivative Test, when possible, to determine the relative extrema. \(f(x)=x^{2} e^{x}\)
Problem 41
A function \(f(x)\) is given. Find the critical points of \(f\) and use the Second Derivative Test, when possible, to determine the relative extrema. . \(f(x)=x^{2} \ln x\)
Problem 42
A function \(f(x)\) is given. Find the critical points of \(f\) and use the Second Derivative Test, when possible, to determine the relative extrema. \(f(x)=e^{-x^{2}}\)
Problem 43
A function \(f(x)\) is given. Find the \(x\) values where \(f^{\prime}(x)\) has a relative maximum or minimum. . \(f(x)=x^{2}-2 x+1\)
Problem 44
A function \(f(x)\) is given. Find the \(x\) values where \(f^{\prime}(x)\) has a relative maximum or minimum. \(f(x)=-x^{2}-5 x+7\)
Problem 45
A function \(f(x)\) is given. Find the \(x\) values where \(f^{\prime}(x)\) has a relative maximum or minimum. \(f(x)=x^{3}-x+1\)
Problem 46
A function \(f(x)\) is given. Find the \(x\) values where \(f^{\prime}(x)\) has a relative maximum or minimum. . \(f(x)=2 x^{3}-3 x^{2}+9 x+5\)
Problem 47
A function \(f(x)\) is given. Find the \(x\) values where \(f^{\prime}(x)\) has a relative maximum or minimum. \(f(x)=\frac{x^{4}}{4}+\frac{x^{3}}{3}-2 x+3\)
Problem 48
A function \(f(x)\) is given. Find the \(x\) values where \(f^{\prime}(x)\) has a relative maximum or minimum. \(f(x)=-3 x^{4}+8 x^{3}+6 x^{2}-24 x+2\)
Problem 49
A function \(f(x)\) is given. Find the \(x\) values where \(f^{\prime}(x)\) has a relative maximum or minimum. \(f(x)=x^{4}-4 x^{3}+6 x^{2}-4 x+1\)
