Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The solution set of <img alt="\mathrm{f^{\prime}(x)>g^{\prime}(x) where \; f(x)=(1 / 2) 5^{2 x+1}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bf%5E%7B%5Cprime%7D%28x%29%3Eg

The solution set of \mathrm{f^{\prime}(x)>g^{\prime}(x) where \; f(x)=(1 / 2) 5^{2 x+1}} and \mathrm{g(x)=5^{x}+4 x \log 5} is

Option: 1

(1, \infty)


Option: 2

(0,1)


Option: 3

[0, \infty)


Option: 4

(0, \infty)


Answers (1)

best_answer

\mathrm{f^{\prime}(x)=(1 / 2) 5^{2 x+1}(\log 5)(2)=\log 5 \cdot\left(5^{2 x+1}\right) also \: g^{\prime}(x)=5^{x} \log 5+4 \log 5}

\mathrm{So \: \left\{x: f^{\prime}(x)>g^{\prime}(x)\right\}=\left\{x: \log 5 \cdot 5^{2 x+1}>\log 55^{x}+4 \log 5\right\}}
                                              \mathrm{=\left\{x: 5^{2 x+1}>5^{x}+4\right\} } 
                                              \mathrm{=\left\{t=5^{x}: 5 t^{2}-t-4>0\right\} }
                                              \mathrm{=\left\{t=5^{x}:(5 t+4)(t-1)>0\right\}}
                                              \mathrm{=\left\{t=5^{x}: t>1 \text { or } t<-4 / 5\right\} }
                                               \mathrm{=\left\{t=5^{x}: t>1\right\}=(0, \infty) }.
 

Posted by

Shailly goel

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JAC Chandigarh Counselling 2025: Round 1 seat allotment result out for BTech admissions
anam-khan

JoSAA round 5 seat allotment result 2025 out on josaa.nic.in
anam-khan

BTech aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today

Latest Question