Applications Of Derivatives Question 9
Question: Let $ P(x)=a_0+a_1x^{2}+a_2x^{4}+…..+a_{n}x^{2n} $ be a polynomial in a real variable x with $ 0<a_0<a_1<a_2<….<a_{n} $ . The function P(x) has
Options:
A) Neither a maximum nor a minimum
B) Only one maximum
C) Only one minimum
D) Only one maximum and only one minimum
Show Answer
Answer:
Correct Answer: C
Solution:
[c] The given polynomial is $ p(x)=a_0+a_1x^{2}+a_2x^{4}+….+a_{n}x^{2n},x\in R $ and $ 0<a_0<a_1<a_2<…..<a_{n}. $
Here, we observe that all coefficients of different powers of x, i.e., $ a_0,a_1,a_2,…..,a_{n}, $ are positive.
Also, only even powers of x are involved. Therefore, P(x) cannot have any maximum value. Moreover, P(x) is minimum, when x = 0, i.e., $ a_0. $ Therefore, P(x) has only one minimum.
BETA
