Q87.Let ๐๐ฅ be a cubic polynomial with ๐1 = - 10, ๐-1 = 6, and has a local minima at ๐ฅ= 1, and ๐'๐ฅ has a local minima at ๐ฅ= - 1 . Then ๐3 is equal to .
What This Question Tests
This question involves using derivative properties for local minima of a cubic polynomial and its first derivative, setting up a system of equations, and solving for the polynomial coefficients.
Concepts Tested
Formulas Used
f'(x) = 0 at local extrema
f''(x) > 0 for local minima
f'''(x) = 0 for local extrema of f'(x)
๐ NCERT Sections This Tests
9.15 โ Apply Mirror Equation And The Condition:
Physics Class 12 ยท Chapter 9
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1.18 A point charge of 2.0 mC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?
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๐ Question Details
- Chapter
- Applications of Derivatives
- Topic
- Local Minima and Maxima
- Year
- 2021
- Shift
- 31 Aug Shift 2
- Q Number
- Q87
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
More from this Chapter
Q87.If p and q are positive real numbers such that p2 + q2 = 1 , then the maximum value of (p + q) is (1) 2 (2) 1/2 (3) 1 (4) โ2 โ2
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Q81.Given P(x) = x4 + ax3 + bx2 + cx + d such that x = 0 is the only real root of P โฒ(x) = 0 . If P(โ1) < P(1), then in the interval [โ1, 1] (1) P(โ1) is the minimum and P(1) is the (2) P(โ1) is not minimum but P(1) is the maximum maximum of P of P (3) P(โ1) is the minimum and P(1) is not the (4) neither P(โ1) is the minimum nor P(1) is the maximum of P maximum of P