Application of Derivatives
Suppose the cube x3px+qhas three distinct real roots where p>0and q>0. Then which one of the following holds?
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Find the value of n∈N
such that the curve (ax)n+(by)n=2
touches the straight line ax+by=2
at the point (a,b)˙
are continuous functions in [a,b]
and are differentiable in(a,b)
then prove that there exists at least one c∈(a,b)
Show that between any two roots of e−x−cosx=0,
there exists at least one root of sinx−e−x=0
The acute angle between the curves y=∣∣x2−1∣∣and y=∣∣x2−3∣∣ at their points of intersection when when x> 0, is
is a real number satisfying the equation 2t3−9t2+30−a=0,
then find the values of the parameter a
for which the equation x+x1=t
gives six real and distinct values of x
If the equation ax2+bx+c=0
has two positive and real roots, then prove that the equation ax2+(b+6a)x+(c+3b)=0
has at least one positive real root.
Find the minimum value of ∣x∣+∣∣x+21∣∣+∣x−3∣+∣∣x−25∣∣˙
Discuss the extremum of