Maxima minima

Question

If the function f(x)=x³+3(a−7)x²+3(a²−9)x−1 has a positive point of maximum, then

Answer 1

\(f(x)=x^3+3(a−7)x^2+3(a^2−9)x−1\)

\(f′(x)=3x^2+6(a−7)x+3(a^2−9)\)

\(D>0,f′(0)>0\)

\(D>0⇒36(a−7)^2−36(a^2−9)>0\)

\(\Rightarrow a < \frac{29}7\)