Question:
Consider the function f(x) = 3x4 – 20x3 – 12x2 + 288x + 1. In which one of the following intervals is the function increasing?
Consider the function f(x) = 3x4 – 20x3 – 12x2 + 288x + 1. In which one of the following intervals is the function increasing?
Options:
- (-3, -2)
- (-2, 3)
- (-4, -3)
- (3, 4)
- (-3, -2)
- (-2, 3)
- (-4, -3)
- (3, 4)
Correct Answer: b)
Explanation:
‘
Gi√en function,
‘ f(z) = 3z* — 202° — 1x2° + 288z + 1
‘ On differentiating w.r.t. x, we get ‘
1 f(z) = 1x2° — 602 — 24x + 288 1
‘ =12 (2® — 5a® — 2z + 24) “
‘ =12(z + 2)(z — 3)(z — 4) ‘
To be increasing f'(z) > 0
‘ ie 12% (z+ 2)(z —3)(z —4) > 0
‘ So, the function is increasing in the inter√al (—2, 3).
1 91
‘ (d) none of these
‘
Gi√en function,
‘ f(z) = 3z* — 202° — 1x2° + 288z + 1
‘ On differentiating w.r.t. x, we get ‘
1 f(z) = 1x2° — 602 — 24x + 288 1
‘ =12 (2® — 5a® — 2z + 24) “
‘ =12(z + 2)(z — 3)(z — 4) ‘
To be increasing f'(z) > 0
‘ ie 12% (z+ 2)(z —3)(z —4) > 0
‘ So, the function is increasing in the inter√al (—2, 3).
1 91
‘ (d) none of these