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Find the maximum and minimum values of t...

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

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To find the maximum and minimum values of the function \( y = 4x^3 - 3x^2 - 6x + 1 \), we will follow these steps: ### Step 1: Find the first derivative We start by differentiating the function with respect to \( x \). \[ y' = \frac{dy}{dx} = \frac{d}{dx}(4x^3 - 3x^2 - 6x + 1) \] ...
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MAHAVEER PUBLICATION-DIFFERENTIATION OR DERIVATIVE OF A FUNCTION-QUESTION BANK
  1. Show that f(x)=x^3-3x^2+15x+2 has no local extremum.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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