Ques3) If a differentiable function f (x) has arelative minimum at x = 0, then the function y = f(x) = ax2+bx+c has a relative minimum at x=0, then which of the following is / are correct :-(a) b = 0 , all a (b) b=0, a> -(1/2) f ' (0) (c) a=0, b=0 (d) a=0 , b=0, c=2.

Y = ax² + bx + c

has max /min at f '(x) = 0

2ax + b = 0

at x=0, we have min. so b=0

also it has rel min. at x = 0

so f "(x) > 0

so ,2a > 0 i.e., a > 0

f '(0) = b =0

so a > -(1/2) f '(0)

a>O

option B

---

Please feel free to post as many doubts on our disucssion forum as you can. If you find any question difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best.

Regards,
Naga Ramesh
IIT Kgp - 2005 batch

f (x) has  arelative minimum at x = 0

That means

f '(0) = 0

or

b=0

.'. f (x) = ax²+c

Also since it is a minima

.'. f"(0) > 0

.'. a>0

Hence the answer is (b)