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1
IIT-JEE 2006
Subjective
+3
-0
If $$f(x)$$ is a twice differentiable function such that $$f(A)=0, f(B)=2, f(C)=-1, f(D)=2$$, $$f(e)=0$$, where $$a < b < c < d < e$$, then the minimum number of zeroes of $$g(x)=\left(f'(x)\right)^{2}+f''(x) f(x)$$ in the interval $$[a, e]$$ is :
2
IIT-JEE 2005
Subjective
+2
-0
If $$\left| {f\left( {{x_1}} \right) - f\left( {{x_2}} \right)} \right| < {\left( {{x_1} - {x_2}} \right)^2},$$ for all $${x_1},{x_2} \in R$$. Find the equation of tangent to the cuve $$y = f\left( x \right)$$ at the point $$(1, 2)$$.
3
IIT-JEE 2005
Subjective
+4
-0
If $$p(x)$$ be a polynomial of degree $$3$$ satisfying $$p(-1)=10, p(1)=-6$$ and $$p(x)$$ has maxima at $$x=-1$$ and $$p'(x)$$ has minima at $$x=1$$. Find the distance between the local maxima and local minima of the curve.
4
IIT-JEE 2004
Subjective
+4
-0
Prove that for $$x \in \left[ {0,{\pi \over 2}} \right],$$ $$\sin x + 2x \ge {{3x\left( {x + 1} \right)} \over \pi }$$. Explain
the identity if any used in the proof.
the identity if any used in the proof.
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