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Prove that the following functions do no...

Prove that the following functions do not have maxima or minima:(i) f (x) = `e ^x` (ii) `g(x) = log x`(iii) `h(x)=x^3+x^2+x+1`

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To prove that the given functions do not have maxima or minima, we will analyze each function by finding its derivative and determining its behavior. ### (i) Function: \( f(x) = e^x \) 1. **Find the derivative**: \[ f'(x) = \frac{d}{dx}(e^x) = e^x \] ...
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NCERT-APPLICATION OF DERIVATIVES-EXERCISE 6.5
  1. Find the maximum and minimum values of x + sin2x on [0,2pi].

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

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

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  4. Find the maximum and minimum values, if any, of the following functio...

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  5. Find the maximum and minimum values, if any, of the following functio...

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  6. Find the local maxima and local minima, if any, of the following func...

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  7. Prove that the following functions do not have maxima or minima:(i) f...

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  8. Find the absolute maximum value and the absolute minimum value of the...

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

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  10. Find both the maximum value and minimum value of 3x^4-8x^3-48 x-25 ...

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

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  12. What is the maximum value of the function sinx + cosx?

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

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

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

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

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

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  18. Show that semi-vertical angle of right circular cone of given surface...

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  19. The point on the curve x^2=2y which is nearest to the point (0, 5) is(...

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

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