Limits Continuity And Differentiability Question 63
Question: Suppose $ f(x)=e^{ax}+e^{bx} $ , where $ a\ne b $ , and that $ f{{}^{n}}(x)-2f’(x)-15f(x)=0 $ for all x. Then the product ab is
Options:
A) 25
B) 9
C) -15
D) -9
Show Answer
Answer:
Correct Answer: C
Solution:
$ (a^{2}-2a-15)e^{ax}+(b^{2}-2b-15)e^{bx}=0 $
$ or(a^{2}-2a-15)=0andb^{2}-2b-15=0 $
$ or(a-5)(a+3)=0and(b-5)(b+3)=0 $ i.e., $ a=5 $
or $ -3 $ and $ b=5 $
or $ -3 $
$ \therefore a\ne b $ .
Hence, $ a=5 $ and $ b=-3 $
or $ a=-3 $ and $ b=5 $
or $ ab=-15 $ .
BETA
