KCET · Maths · Functions
The local minimum value of the function \(f^{\prime}\) given by \(f(x)=3+|x|\), \(x \in R\) is.
- A \( \square 3 \)
- B \( \square 0 \)
- C \( \square -3 \)
- D \( \square 1 \)
Answer & Solution
Correct Answer
(D) \( \square 1 \)
Step-by-step Solution
Detailed explanation
Given that, \(f(x)=3+|x|\) We know that \(|x|=\sqrt{x^{2}}\) So, \(f(x)=3+\sqrt{x^{2}}\)
So, \(f^{\prime}(x)=\frac{2 x}{2 \sqrt{x^{2}}}=\frac{x}{|x|}\)
Clearly when \(x>0\),local minimum \(=1\)
When \(x < 0\), local minimum \(=-1\)
So, option (3) and (4) both are true
So, \(f^{\prime}(x)=\frac{2 x}{2 \sqrt{x^{2}}}=\frac{x}{|x|}\)
Clearly when \(x>0\),local minimum \(=1\)
When \(x < 0\), local minimum \(=-1\)
So, option (3) and (4) both are true
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(f:[2, \infty) \rightarrow R\) be the function defined \(f(x)=x^{2}-4 x+5\), then the ranges of \(f\) isKCET 2020 Medium
- The area of triangle with vertices \( (\mathrm{K}, 0),(4,0),(0,2) \) is \( 4 \) square units, then value of \( \mathrm{K} \) isKCET 2017 Easy
- \(\lim _{x \rightarrow 0} \frac{x 2^{x}-x}{1-\cos x}\) is equal toKCET 2012 Easy
- If the circles \(x^{2}+y^{2}-2 x-2 y-7=0\) and \(x^{2}+y^{2}+4 x+2 y+k=0\) cut orthogonally, then the length of the common chord of the circles isKCET 2007 Hard
- Let the functions " f " and " g " be \(\mathrm{f}:\left[0, \frac{\pi}{2}\right] \rightarrow \mathrm{R}\) given by \(\mathrm{f}(\mathrm{x})=\sin \mathrm{x}\) and \(\mathrm{g}:\left[0, \frac{\pi}{2}\right] \rightarrow \mathrm{R}\) given by \(g(x)=\cos x\), where \(R\) is the set of real numbers
Consider the following statements:
Statement (I): f and g are one-one
Statement (II): \(\mathrm{f}+\mathrm{g}\) is one-one
Which of the following is correct?KCET 2025 Medium - The domain of the function \( f: R \rightarrow R \) defined by \( f(x)=\sqrt{x^{2}-7 x+12} \) isKCET 2019 Easy
More PYQs from KCET
- For the reaction \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) at \(373 \mathrm{~K}\) and 1 atm pressureKCET 2009 Medium
- The set \(\{-1,0,1\}\) is not a multiplicative group because of the failure ofKCET 2008 Easy
- Match the following with their pKa values
\begin{array}{|l|l|l|l|}\hline \text{Acid} & \text{pKa} \\\hline \text{(I) Phenol} & \text{16} \\\hline \text{(II) p-Nitrophenol} & \text{0.78} \\\hline \text{(III) Ethyl alcohol} & \text{10} \\\hline \text{(IV) Picric acid} & \text{7.1} \\\hline\end{array}KCET 2025 Medium - Amniocentesis is one of the methodsKCET 2016 Medium
- A certain prism is found to produce a minimum deviation of \( 38^{\circ} . \) It produces a deviation of \( 44^{\circ} \)
when the angle of incidence is either \( 42^{\circ} \) or \( 62^{\circ} \). What is the angle of incidence when it is
undergoing minimum deviation?KCET 2019 Easy - A train is moving slowly on a straight track with a constant speed of \(2 \mathrm{~ms}^{-1}\). A passenger in that train starts walking at a steady speed of \(2 \mathrm{~ms}^{-1}\) to the back of the train in the opposite direction of the motion of the train. So to an observer standing on the platform directly in front of that passenger, the velocity of the passenger appears to beKCET 2010 Hard