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Find both the maximum value and the minimum value of `3x^(4) – 8x^(3) + 12x^(2) – 48x + 25` on the interval [0, 3].

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The correct Answer is:
Minima at x = 2, minimum value = – 39, Maxima at x = 0, maximum value = 25.
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NCERT TAMIL-APPLICATION OF DERIVATIVES-EXERCISE 6.5
  1. Find the absolute maximum value and the absolute minimum value of the ...

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  2. Find the maximum profit that a company can make, if the profit functio...

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  3. Find both the maximum value and the minimum value of 3x^(4) – 8x^(3) +...

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  4. At what points in the interval [0, 2pi], does the function sin 2x atta...

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  5. What is the maximum value of the function sin x + cos x?

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  6. Find the maximum value of 2x^(3) – 24x + 107 in the interval [1, 3]. F...

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  7. It is given that at x = 1, the function x^(4) – 62x^(2) + ax + 9 attai...

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  8. Find the maximum and minimum values of x + sin 2x on [0, 2pi].

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  9. Find two numbers whose sum is 24 and whose product is as large as poss...

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  10. Find two positive numbers x and y such that x + y = 60 and xy^(3) is m...

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  11. Find two positive numbers x and y such that their sum is 35 and the pr...

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  12. Find two positive numbers whose sum is 16 and the sum of whose cubes i...

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  13. A square piece of tin of side 18 cm is to be made into a box without t...

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  14. A rectangular sheet of tin 45 cm by 24 cm is to be made into a box wit...

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  15. Show that of all the rectangles inscribed in a given fixed circle, the...

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  16. Show that the right circular cylinder of given surface and maximum vol...

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  17. Of all the closed cylindrical cans (right circular), of a given volume...

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  18. A wire of length 28 m is to be cut into two pieces. One of the pieces ...

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  19. Prove that the volume of the largest cone that can be inscribed in a s...

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  20. Show that the right circular cone of least curved surface and given vo...

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