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Concavity and convexity : if f''(x) ...

Concavity and convexity :
if `f''(x) gt 0 AA x in (a,b)` then the curve y=f(x) is concave up ( or convex down) in (a,b) and `if f''(x) lt 0 AA x in (a,b)` then the curve y=f(x) is concave down (or convex up ) in (a,b)

Inflection point :
The point where concavity of the curve changes is known as point of inflection (at inflection point `f''(x)` is equal to 0 or undefined)

Exhaustive set of values of 'a' for which the function `f(x) =x^(4) +ax^(3)+(3x^(2))/(2)+1` will be concave upward along the entire real line is : (A) `[-1,1]` (B) `[-2,2]` (C) `[0,2]` (D) `[0,4]`

A

`[-1,1]`

B

`[-2,2]`

C

`[0,2]`

D

`[0,4]`

Text Solution

Verified by Experts

The correct Answer is:
B
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