Maxima and Minima — Maths STD 12 Science — Question
Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMaxima and Minima1 Mark
MCQ
The function $f(x) = 2x^3- 15x^2 + 36x + 4$ is maximum at $x =$
A
$3$
B
$0$
C
$4$
✓
$2$
✓
Answer
Correct option: D.
$2$
Given, $f(x) = 2x^3- 15x^2 + 36x + 4$
lmplies that $f'(x) = 6x^2- 30x + 36$
For a local maxima or a local minima, we must have $f'(x) = 0$
lmplies that $6x^2 - 30x + 36 = 0$
lmplies that $x^2 - 5x + 6 = 0$
$(x - 2)(x - 3) = 0$
lmplies that $x = 2, 3$
Now, $f''(x) = 12x - 30$
lmplies that $f''(2) = 24 - 30 = 6 < 0$
Therefore, $x = 1$ is a local maxima.
Also,$f''(3) = 36 - 30 = 6 > 0$
Therefore, $x = 2$ is a local maxima.
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