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If the curve f(x)=x(x+3)e^(-x/2) has its...

If the curve `f(x)=x(x+3)e^(-x/2)` has its local extremum at `x=d` then

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The function f(x)=x(x+4)e^(-x//2) has its local maxima at x=adot Then (a) a=2sqrt(2) (b) a=1-sqrt(3) (c) a=-1+sqrt(3) (d) a=-4

The function f(x)=x(x+4)e^(-x//2) has its local maxima at x=adot Then (a) a=2sqrt(2) (b) a=1-sqrt(3) (c) a=-1+sqrt(3) (d) a=-4

The function f(x)=x(x+4)e^(-x//2) has its local maxima at x=adot Then (a) a=2sqrt(2) (b) a=1-sqrt(3) (c) a=-1+sqrt(3) (d) a=-4

The function f(x)=x(x+4)e^(-x/2) has its local maxima at x=a* Then (a)a=2sqrt(2)(b)a=1-sqrt(3)(c)a=-1+sqrt(3)(d)a=-4

The function f(x)=e^(x^(3)-6x^(2)+10) attains local extremum at x = a and x = b (a < b), then the value of a+b is equal to

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Statement I :The function f(x)=(x^(3)+3x-4)(x^(2)+4x-5) has local extremum at x=1. Statement II :f(x) is continuos and differentiable and f'(1)=0.

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Statement I :The function f(x)=(x^(3)+3x-4)(x^(2)+4x-5) has local extremum at x=1. Statement II :f(x) is continuos and differentiable and f'(1)=0.

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