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

Let f be an even function and let f ’ (0) exist . then find f ‘ (0)

Let f be an even function and let f ’ (0) exist . 
then find f ‘ (0) 

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
f(x) = f(-x)
f'(x) = \lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}
f’(0) exist. So
LHD (x=0) = RHD (x=0)
\lim_{h\rightarrow 0}\frac{f(-h)-f(0)}{-h} = \lim_{h\rightarrow 0}\frac{f(h)-f(0)}{h}
f(-h) = f(h)
\lim_{h\rightarrow 0}\frac{f(h)-f(0)}{-h} = \lim_{h\rightarrow 0}\frac{f(h)-f(0)}{h}
Both are zero by zero form. So apply L’Hospital rule,
\lim_{h\rightarrow 0}-f'(h) = \lim_{h\rightarrow 0}f'(h)
-f'(0) = f'(0)
f'(0) = 0
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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

10th iCAT Scholarship Test Registration Form