1

IIT-JEE 1997

Subjective

+5

-0

Let $$a+b=4$$, where $$a<2,$$ and let $$g(x)$$ be a differentiable function.

If $${{dg} \over {dx}} > 0$$ for all $$x$$, prove that $$\int_0^a {g\left( x \right)dx + \int_0^b {g\left( x \right)dx} } $$

increases as $$(b-a)$$ increases.

2

IIT-JEE 1996

Subjective

+5

-0

A curve $$y=f(x)$$ passes through the point $$P(1, 1)$$. The normal to the curve at $$P$$ is $$a(y-1)+(x-1)=0$$. If the slope of the tangent at any point on the curve is proportional to the ordinate of the point, determine the equation of the curve. Also obtain the area bounded by the $$y$$-axis, the curve and the normal to the curve at $$P$$.

3

IIT-JEE 1996

Subjective

+5

-0

Determine the points of maxima and minima of the function

$$f\left( x \right) = {1 \over 8}\ell n\,x - bx + {x^2},x > 0,$$ where $$b \ge 0$$ is a constant.

$$f\left( x \right) = {1 \over 8}\ell n\,x - bx + {x^2},x > 0,$$ where $$b \ge 0$$ is a constant.

4

IIT-JEE 1996

Subjective

+3

-0

Let $$f\left( x \right) = \left\{ {\matrix{
{x{e^{ax}},\,\,\,\,\,\,\,x \le 0} \cr
{x + a{x^2} - {x^3},\,x > 0} \cr
} } \right.$$

Where a is a positive constant. Find the interval in which $$f'(x)$$ is increasing.

Questions Asked from Application of Derivatives (Subjective)

Number in Brackets after Paper Indicates No. of Questions

IIT-JEE 2006 (1)
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IIT-JEE 2003 (4)
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IIT-JEE 1996 (3)
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IIT-JEE 1982 (2)
IIT-JEE 1981 (3)
IIT-JEE 1979 (1)

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