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Let f be a function defined on [a, b] su...

Let f be a function defined on `[a, b]` such that `f'(x)>0` for all `x in (a,b)`. Then prove that f is an increasing function on `(a, b)`.

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MODERN PUBLICATION-APPLICATION OF DERIVATIVES-EXERCISE
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  2. Find the rate of change of the area of a circle with respect to its ra...

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  3. Find the rate of change of the area of a circle with respect to its ra...

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  4. An edge of a variable cube is increasing at the rate of 3 cm/s. How fa...

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  5. The radius of a soap-bubble is increasing at the rate of 0.2cm/s. Find...

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  6. The radius of a circle is increasing at the rate of 0.7 cm/s. What is ...

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  7. The radius of a circle is increasing uniformly at the rate of 4 cm per...

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  8. If the area of a circle increases uniformly, then show that the rate o...

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  9. The radius of a circle is increasing uniformly at the rate of 3 cm/s. ...

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  10. The radius of an air bubble is increasing at the rate of 1/2 cm/s. At...

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  11. The radius of spherical balloon is increasing at the rate 5 cm per sec...

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  12. The radius of a spherical soap bubble is increasing at the rate of 0.3...

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  13. A balloon, which always remains spherical, has a variable diameter 3/2...

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  14. A balloon, which always remains spherical on inflation, is being infla...

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  15. The volume of a cube is increasing at the rate of 9 "cm"^(3)//sec. How...

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  16. The volume of a cube is increasing at the rate of 8 cm^3/s. How fast i...

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  17. The volume of a cube is increasing at the rate of 7 cubic metre per se...

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  18. A particle moves along the curve y=4/(3)x^(3)+5. Find the points on th...

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  19. A particle move along the curve 6y = x^3 +2. Find the points on the cr...

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  20. The radius of a cylinder increases at the rate of 1 cm/s and its heigh...

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  21. The contentment obtained after eating X-units of a new dish at a trial...

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