Application of Derivatives
Late a∈Rand let f:Rbe given by f(x)=x5−5x+a,thenf(x)has three real roots if a>4f(x)has only one real roots if a>4f(x)has three real roots if a<−4f(x)has three real roots if −4<a<4
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A private telephone company serving a small community makes a profit of Rs. 12.00 per subscriber, if it has 725 subscribers. It decides to reduce the rate by a fixed sum for each subscriber over 725, thereby reducing the profit by 1 paise per subscriber. Thus, there will be profit of Rs. 11.99 on each of the 726 subscribers, Rs. 11.98 on each of the 727 subscribers, etc. What is the number of subscribers which will give the company the maximum profit?
Find the shortest distance between the line y=x−2
and the parabola y=x2+3x+2.
Discuss the maxima and minima of the function f(x)=x32−x34˙
Draw the graph of y=f(x)
and find the range of f(x)˙
On the curve x3=12y,
find the interval of values of x
for which the abscissa changes at a faster rate than the ordinate?
If the curves ay+x2=7andx3=y
cut orthogonally at (1,1)
, then find the value a˙
For the curve xy=c,
prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.
Prove that ∣∣tan−1x−tan−1y∣∣≤∣x−y∣∀x,y∈R˙
Find the values of p