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Find the absolute maximum value and the absolute minimum value of the followingfunctions in the given intervals:(i) `f(x)=x^2,x in [-2,2]` (ii) `f(x)=sinx+cosx ,x in [0,pi]

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To find the absolute maximum and minimum values of the given functions in the specified intervals, we will follow these steps: ### (i) For the function \( f(x) = x^2 \) in the interval \([-2, 2]\): **Step 1: Find the derivative of the function.** \[ f'(x) = 2x \] ...
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NAGEEN PRAKASHAN ENGLISH-APPLICATIONS OF DERIVATIVES-Exercise 6.5
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  2. Prove that the following functions do not have maxima or minima:(i) f...

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  4. Find the maximum profit that a company can make, if the profit functi...

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  6. At what points in the interval [0,""""2pi] , does the function s in" "...

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  7. What is the maximum value of the function s in" "x" "+" "cos" "x ?

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  8. Find the maximum value of 2x^3-24 x+107in the interval [1, 3]. Find t...

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  9. It is given that at x=1 , the function x^4-62 x^2+a x+9 attains its ma...

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  10. Find the maximum and minimum values of f(x)=x+sin2x in the interval...

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  11. Find two numbers whose sum is 24 and whose product is as large as p...

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  12. Find two positive numbers x and y such that x+y=60 and x y^3 is max...

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  13. Find two positive numbers x and y such that their sum is 35 and ...

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  14. Find two positive numbers whose sum is 16 and the sum of whose cube...

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  15. A square piece of tin of side 18 cm is to be made into a box w...

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

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  17. Show that of all the rectangles inscribed in a given circle, the sq...

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  18. Show that the height of a closed right circular cylinder of given s...

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

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

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