AP EAMCET · Maths · Continuity and Differentiability
Let \(\mathrm{f}(x)=\min \left\{x, x^2\right\}\) for every real number of \(x\). then
- A \(f(x)\) is continuous for all \(x\)
- B \(f(x)\) is differentiable for all \(x\)
- C \(f^{\prime}(x)=2\) for all \(x\gt1\)
- D \(f(x)\) is not differentiable at three values of \(x\)
Answer & Solution
Correct Answer
(A) \(f(x)\) is continuous for all \(x\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} f(x) & =\min \left\{x, x^2\right\} \\ & =\left\{\begin{array}{ccc}x & \text { if } & x \lt 0 \\ x^2 & \text { if } & 0 \leq x \lt 1 \\ x & \text { if } & 1 \lt x\end{array}\right.\end{aligned}\)…
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
- If \(n\) is a positive integer, then \((1+i \sqrt{3})^n+(1-i \sqrt{3})^n\) is equal toAP EAMCET 2021 Medium
- The value of \(\cos \frac{2 \pi}{15} \cos \frac{4 \pi}{15} \cos \frac{8 \pi}{15} \cos \frac{14 \pi}{15}\) is :AP EAMCET 2003 Easy
- If \(\lim _{x \rightarrow \infty}\left\{\frac{x^3+1}{x^2+1}-(\alpha x+\beta)\right\}\) exists and equal to 2 , then the ordered pair \((\alpha, \beta)\) of real numbers isAP EAMCET 2019 Medium
- Find the absolute maximum of \(x^{40}-x^{20}\) on the interval \([0,1]\).AP EAMCET 2021 Hard
- Suppose the pairs of straight lines \(2 x^2+a x y+3 y^2=0\) and \(2 x^2+b x y-3 y^2=0\) are such that they have one common line with the other two remaining perpendicular. Then the values of \(a\) and \(b\) respectively areAP EAMCET 2022 Medium
- When the coordinate axes are rotated through an angle of \(45^{\circ}\) about the origin in the positive direction, if the transformed equation of a curve is \(17 x^2-16 x y+17 y^2=225\), then the original equation of that curve isAP EAMCET 2018 Medium
More PYQs from AP EAMCET
- A rubber cube of side \(5 \mathrm{~cm}\) has one face fixed, while a tangential force \(1800 \mathrm{~N}\) is applied on its opposite face. If modulus of rigidity of rubber is \(2.4 \times 10^6 \mathrm{Nm}^{-2}\), then the lateral displacement of the strained face is ________AP EAMCET 2018 Medium
- The perpendicular distance from the point \((1,2)\) to common chord of the circles \(x^2+y^2-2 x+4 y-4=0\) and \(x^2+y^2+4 x-6 y-3=0\) is........ units.AP EAMCET 2021 Medium
- If the pair of straight lines \(x y-x-y+1=0\) and the line \(a x+2 y-3 a=0\) are concurrent, then \(a\) is equal toAP EAMCET 2002 Medium
- If \(y=(\log x)^{1 / x}+x^{\log x}\), at \(x=e, \frac{d y}{d x}=\)AP EAMCET 2025 Medium
- If \(\int \frac{3 \cos x-2 \sin x}{4 \sin x+5 \cos x} d x=A \log\)
\(|5 \cos x+4 \sin x|+B x+c\), then \(A\) and \(B\) areAP EAMCET 2021 Medium - \(1-\frac{2}{3}+\frac{2.4}{3.6}-\frac{2.4 .6}{3.6 .9}+\ldots \infty=\)AP EAMCET 2024 Easy