1
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.
2
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.

3
IIT-JEE 1995
Subjective
+5
-0
Let $$(h, k)$$ be a fixed point, where $$h > 0,k > 0.$$. A straight line passing through this point cuts the possitive direction of the coordinate axes at the points $$P$$ and $$Q$$. Find the minimum area of the triangle $$OPQ$$, $$O$$ being the origin.
4
IIT-JEE 1994
Subjective
+5
-0
The curve $$y = a{x^3} + b{x^2} + cx + 5$$, touches the $$x$$-axis at $$P(-2, 0)$$ and cuts the $$y$$ axis at a point $$Q$$, where its gradient is $$3$$. Find $$a, b, c$$.
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