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if a function f is (i) continuous on ...

if a function f is
(i) continuous on [a,b]
(ii) derivable on (a,b) and
(iii) f(x) `gt 0 x in (a,b)` then show that f(x) is strictly increasing on [a,b]

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RESONANCE-APPLICATION OF DERIVATIVES-Self Practice Problems
  1. For each of the following graph comment on monotonically of f(x) ...

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  2. Let f(x)=x^3-3x^2+ 3x + 4, comment on the monotonic behaviour of f(x) ...

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  3. Draw the graph of function f(x)={underset([x] " "1 le x le 2)(x " ...

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  4. In each of following graphs identify if x= a is point of local maxi...

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  5. Examine the graph of following functions in each case identify the p...

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  6. Find the points of local maxima or minima of following functions...

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  7. Let f(x) =x^(3) =x^(2) -x-4 (i) find the possible points of maxim...

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  8. Let f(x) =x +(1)/(x). find local maximum and local minimum value ...

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  9. if f(x) ={underset( cos x " "x le 0)((x+lambda)^(2) " " x lt 0). ...

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  10. Let f(x) = sin x (1+cos x) , x in (0,2pi). Find the number of criti...

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  11. Find the two positive numbers x and y whose sum is 35 and the ...

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

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

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  14. The maximum distance of the centre of the ellipse x^2/(81)+y^2/(25)=1 ...

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  15. A line is drawn passing through point P(1,2) to cut positive coord...

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  16. Two towns A and B are situated on the same side of a straight road at ...

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  17. if f (x) satisfies condition in Rolle's theorem then show that betw...

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  18. Show that for any real numbers lambda, the polynomial P(x)=x^7+x^3+lam...

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  19. Using LMVT, prove that if two functions have equal derivatives at all ...

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  20. if a function f is (i) continuous on [a,b] (ii) derivable on (a,b...

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