If the interval in which the function $f(x) = 4x^3-6x^2-72x+30$ is strictly decreasing, is (a, b) then a + b is equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1
Given: $f(x) = 4x^3 - 6x^2 - 72x + 30$
Compute derivative:
$f'(x) = \frac{d}{dx}(4x^3 - 6x^2 - 72x + 30) = 12x^2 - 12x - 72$
Set $f'(x) < 0$ for decreasing:
$12x^2 - 12x - 72 < 0$
Divide by 12:
$x^2 - x - 6 < 0$
Factor:
$(x - 3)(x + 2) < 0$
Solution of inequality:
$x \in (-2,\ 3)$
Interval of strictly decreasing = $(-2,\ 3)$
$a + b = -2 + 3 = 1$