JEE Mains · Maths · STD 12 - 6. Application of derivatives
If \(\mathrm{p}(\mathrm{x})\) be a polynomial of degree three that has a local maximum value \(8\) at \(x=1\) and a local minimum value \(4\) at \(x=2 ;\) then \(p(0)\) is equal to
- A \(12\)
- B \(-24\)
- C \(06\)
- D \(-12\)
Answer & Solution
Correct Answer
(D) \(-12\)
Step-by-step Solution
Detailed explanation
since \(\mathrm{p}(\mathrm{x})\) has realtive extreme at \(x=1 \& 2\) so \(\mathrm{p}^{\prime}(\mathrm{x})=0\) at \(\mathrm{x}=1 \& 2\) \(\Rightarrow \mathrm{p}^{\prime}(\mathrm{x})=\mathrm{A}(\mathrm{x}-1)(\mathrm{x}-2)\)…
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
- The mean of the data set comprising of \(16\) observations is \(16.\) If one of the observation valued \(16\) is deleted and three new observations valued \(3, 4\) and \(5\) are added to the data, then the mean of the resultant data, is:JEE Mains 2015 Medium
- Let \(\mathrm{x}^{\mathrm{k}}+\mathrm{y}^{\mathrm{k}}=\mathrm{a}^{\mathrm{k}},(\mathrm{a}, \mathrm{K}>0)\) and \(\frac{\mathrm{dy}}{\mathrm{dx}}+\left(\frac{\mathrm{y}}{\mathrm{x}}\right)^{\frac{1}{3}}=0\) then \(\mathrm{k}\) isJEE Mains 2020 Hard
- If the vectors \(\vec{a}=\lambda \hat{i}+\mu \hat{j}+4 \hat{k}, \vec{b}=2 \hat{i}+4 \hat{j}-2 \hat{k}\) and \(\vec{c}=2 \hat{i}+3 \hat{j}+\hat{k}\) are coplanar and the projection of \(\vec{a}\) on the vector \(\vec{b}\) is \(\sqrt{54}\) units, then the sum of all possible values of \(\lambda+\mu\) is equal toJEE Mains 2023 Hard
- The angle of elevation of the top of a vertical tower from a point \(P\) on the horizontal ground was observed to be \(\alpha \). After moving a distance \(2\, metres\) from \(P\) towards the foot of the tower, the angle of elevation changes to \(\beta \). Then the height (in metres) of the tower isJEE Mains 2014 Hard
- The value of \(\sum_{n=1}^{100} \int_{n-1}^{n} e^{x-[x]} d x,\) where \([x]\) is the greatest integer \(\leq x ,\) isJEE Mains 2021 Medium
- The cost of running a bus from \(A\) to \(B\), is \(Rs.\,\left( {av + \frac{b}{v}} \right)\). where \(v\, km/ h\) is the average speed of the bus. When the bus travels at \(30\, km/h\), the cost comes out to be \(Rs.\, 75\) while at \(40\, km/h\), it is \(Rs.\,65\) . Then the most economical speed (in \(km/ h\)) of the bus isJEE Mains 2013 Hard
More PYQs from JEE Mains
- The shortest distance between the point \(\left( {\frac{3}{2},0} \right)\) and the curve \(y = \sqrt x ,\left( {x > 0} \right)\), isJEE Mains 2019 Hard
- Let \(L\) denote the line in the \(xy\)-plane with \(x\) and \(y\) intercepts as \(3\) and \(1\) respectively. Then the image of the point \((-1,-4)\) in this line isJEE Mains 2020 Hard
- Out of \(60 \%\) female and \(40 \%\) male candidates appearing in an exam, \(60\%\) candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it. A candidate is randomly chosen from the qualified candidates. The probability, that the chosen candidate is a female, is.JEE Mains 2022 Medium
- If \(f : R \rightarrow R\) be a continuous function satisfying \(\int \limits_0^{\pi / 2} f(\sin 2 x) \cdot \sin x d x+\alpha \int \limits_0^{\pi / 4} f(\cos 2 x) \cdot \cos x d x=0\)then \(\alpha\) is equal toJEE Mains 2023 Hard
- The integral \(\int {\sqrt {1 + 2\cot \,x\,\left( {\cos ec\,x + \cot \,x} \right)} \,dx} \) \(\left( {0 < x < \frac{\pi }{2}} \right)\) is equal to ( where \(C\) is a constant of integration)JEE Mains 2017 Hard
- Let \(P\) be a point on the parabola, \(x^2 = 4y.\) If the distance of \(P\) from the centre of the circle, \(x^2 + y^2 + 6x + 8 = 0\) is minimum, then the equation of the tangent to the parabola at \(P,\) isJEE Mains 2018 Hard