Multiple choice

A point on a curve is said to be an extremum if it is a local minimum or a local maximum. What is the number of distinct extrema for the curve 3x4 − 16x3 + 24x2 + 37?

  1. 0

  2. 1

  3. 2

  4. 3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

F(x) = 3x4 –16x3 + 24x2 + 37 f1 (x) = 12x3 – 48x2 + 48x Here, f1 (x) = 0 $\Rightarrow$ x3 – 4x2 + 4x = 0 $\Rightarrow$ x(x – 2)2 = 0 $\therefore$ x = 0, 2, 2 

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