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let f(x)=1+2x^2+2^2x^4+.....+2^(10)x^(20...

let `f(x)=1+2x^2+2^2x^4+.....+2^(10)x^(20).` The , `f(x)` has

A

more than one minimum

B

exactly one minimum

C

at least one maximum none of these

D

neither a maximum nor a minimum

Text Solution

Verified by Experts

The correct Answer is:
B
We have
`f(x)=1+2x^2+x^4+...+2^10x^20`
`rArr f(x)=x(4+4.2^2.x^2+…..+20.2^(10)x^(18))`
Clearly.f(x)=0 at x =0 only and `f(0) gt 0`
Hence ,f(x) has exactly one minimum.
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