HARD
JEE Main/Advance
IMPORTANT
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For the function f(x)=xcos1x, x1

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Important Questions on Application of Derivatives

HARD
JEE Main/Advance
IMPORTANT
Let f, g, h be real valued functions defined on the interval 0,1 by fx=ex2+e-x2, gx=xex2+e-x2 and hx=x2ex2+e-x2. If a, b and c denote, respectively, the absolute maximum of f, g and h on 0,1, then
HARD
JEE Main/Advance
IMPORTANT
The number of points in (-,) for which x2-xsinx-cosx=0 is 
HARD
JEE Main/Advance
IMPORTANT
A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8:15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. The lengths of the sides of the rectangular sheet are
HARD
JEE Main/Advance
IMPORTANT
The function f(x)=2|x|+|x+2|-|| x+2|-2|x|| has a local minimum or a local maximum at x equal to 
HARD
JEE Main/Advance
IMPORTANT
Let aR and f:RR be given by f(x)=x5-5x+a, then
MEDIUM
JEE Main/Advance
IMPORTANT
The slope of the tangent to the curve y-x52=x1+x22 at the point (1,3) is
HARD
JEE Main/Advance
IMPORTANT
Let f:R(0,) and g:RR be twice differentiable functions such that f" and g" are continuous functions on R. Suppose f'(2)=g(2)=0,f"(2)0 and g'(2)0, If limx2f(x)g(x)f'(x)g'(x)=1, then
HARD
JEE Main/Advance
IMPORTANT
If f: RR is a differentiable function such that f'(x)>2f(x) for all xR, and f(0)=1 then