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Show that f(x)=1+x+x^2+x^3 has no local ...

Show that `f(x)=1+x+x^2+x^3` has no local extremum.

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MAHAVEER PUBLICATION-DIFFERENTIATION OR DERIVATIVE OF A FUNCTION-QUESTION BANK
  1. Show that f(x)=3x-x^3 has a local maximum at x=1.

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  2. Show that f(x)=x^2+(250)/x has a local minimum at x=5.

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  3. Show that f(x)=1+x+x^2+x^3 has no local extremum.

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  4. Show that f(x)=x^3-3x^2+15x+2 has no local extremum.

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  5. Find the extreme values of the function y=2x^3-9x^2+12x+5

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  6. Find the maximum and minimum values of the function y=4x^3-3x^2-6x+1

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  7. Find two positive numbers x and y such that x+y=28 and xy is maximum.

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  8. Find two positive numbers x and y such that x+y=64 and x^3+y^3 is min...

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  9. Find two positive numbers x and y such that x+y=400 and xy^3 is maxim...

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  10. Find two positive numbers x and y such that xy=36 and x+y is minimum.

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  11. Find the point on the curve y^2=4x which is nearest to the point...

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

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  13. Show that the largest rectangle with a given perimeter is a square.

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

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  15. Show that the triangle of maximum area that can be inscribed in a g...

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  16. Consider an ellipse x^(2)/a^(2) + y^(2)/b^(2)=1 What is the area of ...

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  17. Let A P and B Q be two vertical poles at points A and B respectivel...

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  18. If the length of three sides of a trapezium other than base are equ...

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  19. Show if f(x)=|x| is differentiable for all x.

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  20. If f(x) and g(x) are differentiable for all, x then d/dx(f(g(x)))=f'(...

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