Question
Mathematics Question on types of differential equations
Let f(x) = |(x – 1)(x2 – 2x – 3)| + x – 3, x ∈ R. If m and M are, respectively the number of points of local minimum and local maximum of f in the interval (0, 4), then m + M is equal to
Answer
The correct answer is: 3
f(x) = |(x – 1)(x2 – 2x – 3)| + x – 3
\left\\{\begin{matrix} (x-3)(x^2)&3\leq x\leq 4 \\\ (x-3)(2-x^2) &1\leq x< 3 \\\ (x-3)(x^2)& 0 < x< 1 \end{matrix}\right.
\left\\{\begin{matrix} 3x^2-6x&3< x< 4 \\\ -3x^2-6x+2 &1< x< 3 \\\ 3x^2-6x& 0 < x< 1 \end{matrix}\right.
at one point → Maximum
x∈(3,4)f′(x)≠0
x∈(0,1)f′(x)≠0
So, 3 points