Q81.If ๐1 and ๐2 are respectively the sets of local minimum and local maximum points of the function, ๐๐ฅ= 9๐ฅ4 + 12๐ฅ3 - 36๐ฅ2 + 25, ๐ฅโ๐ , then (1) ๐1 = -2; ๐2 = {0,1} (2) ๐1 = -1; ๐2 = 0,2 (3) ๐1 = -2,0; ๐2 = {1} (4) ๐1 = -2,1; ๐2 = {0}
What This Question Tests
The question tests the application of first and second derivative tests to identify local maximum and local minimum points of a polynomial function.
Concepts Tested
Formulas Used
f'(x) = 0 for critical points
f''(x) > 0 for local minimum
f''(x) < 0 for local maximum
๐ NCERT Sections This Tests
9.15 โ Apply Mirror Equation And The Condition:
Physics Class 12 ยท Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
1.3 โ Define The Following Terms:
Chemistry Class 11 ยท Chapter 1
1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.
9.1 โ A Small Candle, 2.5 Cm In Size Is Placed At 27 Cm In Front Of A Concave
Physics Class 12 ยท Chapter 9
9.1 A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?
๐ Question Details
- Chapter
- Applications of Derivatives
- Topic
- Local maxima and minima
- Year
- 2019
- Shift
- 08 Apr Shift 1
- Q Number
- Q81
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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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