Question-5 If f(x)=x^{2}-3 x, then the points at which f(x)=f^{\prime}(x)are
A) 1, 3
B) 1, -3
C) -1, 3
D) None
Answer: D) None
Explanation
Given f(x)=x^{2}-3 x
\Rightarrow f^{\prime}(x)=2 x-3According to the question, f(x)=f^{\prime}(x)
\Rightarrow x^{2}-3 x=2 x-3 \Rightarrow x^{2}-5 x+3=0 \Rightarrow x=\frac{5 \pm \sqrt{25-12}}{2}=\frac{5 \pm \sqrt{13}}{2}.
Hence, the solutions are \frac{5+\sqrt{13}}{2} \& \frac{5-\sqrt{13}}{2}.