Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

Ques3) If a differentiable function f (x) has arelative minimum at x = 0, then the function y = f(x) = ax 2 +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.

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.

Grade:12

2 Answers

Ramesh V
70 Points
11 years ago

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

Askiitian.Expert Rajat
24 Points
11 years ago

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)

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free