The minimum value of f(a) = (2 a^2 - 3) + 3(3 - a) + 4 is - Vidyadip

MCQ

The minimum value of $f(a) = (2{a^2} - 3) + 3(3 - a) + 4$ is

A
${{15} \over 2}$
B
${{11} \over 2}$
C
${{ - 13} \over 2}$
✓
${{71} \over 8}$

✓

Answer

Correct option: D.

${{71} \over 8}$

d
(d) $f(a) = 2{a^2} - 3a + 10$

$f'(a) = 4a - 3,f(a) = 4 > 0$

for exteremum, $f'(a) = 0 \Rightarrow a = \frac{3}{4}$

$\therefore$ $f(a)$ is minimum at $a = \frac{3}{4}$

$f{(a)_{\min }} = 2 \times {\left( {\frac{3}{4}} \right)^2} - 3 \times \left( {\frac{3}{4}} \right) + 10 = \frac{{71}}{8}$.

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