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Using examples, prove that the condition...

Using examples, prove that the condition`dy/dx = 0` is neither a necessary nor a sufficient condition for a function `y = f(x)` to have a maximum or a minimumat a point.

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A DAS GUPTA-Maxima and Minima-EXERCISE
  1. f (x) =2x -tan ^(-1) x - ln (x+ sqrt(1+ x ^(2)))

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  2. Show that f(x) = sqrt(e^(x^(2))-1) has its extremum at x = 0. Also me...

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  3. Using examples, prove that the conditiondy/dx = 0 is neither a necessa...

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  4. Let f(x) = x ^3 - 12x. Prove that the equation x^3 - 12x - k = 0 has a...

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  5. If y=a log x +bx^(2)+x has its exteme values at x=-1 and x=2, then fin...

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  6. If y=(a x-b)/((x-1)(x-4)) has a turning point P(2,-1), find the value ...

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  7. Find the shortest distance of the point (0, c) from the parabola y=x^...

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  8. Find the coordinates of a point on the parabola y=x^2+7x+2 which is cl...

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  9. Given an interior point A on the axis of the parabola y ^2 = 2px, (p >...

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  10. Find the coordinates of the point on the curve y=x/(1+x^2) where the t...

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  11. The parametric equations of the curve are x=2t(t^2+3)-3t^2, y=2t(t^2+3...

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  12. A function is defined parametrically as follows :x=t^5-5t^3-20 t+7y=4t...

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  13. Let (h , k) be a fixed point, where h >0,k > 0. A straight line passin...

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  14. A 12-cm-long wire is bent to form a triangle with one of the angles as...

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  15. The largest area of a rectangle which has one side on the x-axis and t...

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  16. Three sides of a trapezium are each equal to k cm. Find the greatest p...

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  17. A statue 4 meters high sits on a column 5.6 meters high . How far f...

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  18. A wire of length l is cut into two parts. One part is bent into a circ...

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  19. A point P is given on the circumference of a circle of radius rdot Cho...

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  20. The circle x^2+y^2=1 cuts the x-axis at Pa n dQdot Another circle with...

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