Calculus - Application o derivatives

62

first is kind of straightforward...

derivative is zero at 2, f(2)=-1

and the double derivative is +ve or zero.. (if it turns to be zero.. then go for the sign test)

62

take a tangent to xy=-1

then find the condition of repeated roots with the first curve

(hint for the second problem)

49

for no 3!

draw graph to get maxima and minima!

else consider the points(without the graph)::
1) derivative=0
2) end points!!!

bascally we have to find maxima and minima! by any method that is!

11

For no 3, consider g(x)=x-sinx-a
Thus,g'(x)=1-cos>0
Thus g(x) is increasing.
Therefore to have a root between (-pi/2,pi/2),
g(-pi/2)*g(pi/2)<0

Hence,c is the correct answer.

Application o derivatives