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Show that the largest rectangle with a g...

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

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To show that the largest rectangle with a given perimeter is a square, we will follow these steps: ### Step 1: Define the Variables Let the length of the rectangle be \( x \) and the width be \( y \). The perimeter \( P \) of the rectangle is given by the formula: \[ P = 2x + 2y \] ...
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MAHAVEER PUBLICATION-DIFFERENTIATION OR DERIVATIVE OF A FUNCTION-QUESTION BANK
  1. Find the point on the curve y^2=4x which is nearest to the point...

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

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

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

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

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

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

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

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

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

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  11. If f is differentiable, then d/dxf(sqrtx)=(f'(sqrtx))/(2sqrtx).

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  12. Derive d/dx(tanx)=sec^2 x

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  13. If f(x)=(1+x)(1+x^2)(1+x^3)(1+x^4), then f'(0)=1

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  14. If f(x)=7x-8, then f'(3)=

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  15. Show that the equation of the tangent line to the parabola y=x^2 at (-...

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  16. Write True/False: If for any function y=f(x), f'( c )=0, then the ta...

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  17. If f'(x)=1/(3-x)^2, the equation of the tangent line to f(x) at (0, 1/...

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  18. Write True/False: All critical points of f(x) satisfy f'(x)=0

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  19. Write True/False: If f'( c ) does not exist and f'(x) changes from po...

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  20. Write True/False: If f'( c ) exists and f'( c )gt0, then f(x) has a l...

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