Q14 of 137 Page 18

Find the points of local maxima or local minima, if any, of the following functions, using the first derivative test. Also, find the local maximum or local minimum values, as the case may be:

We have, f(x) =


Differentiate w.r.t x, we get,


f ‘(x) =


For the point of local maxima and minima,


f ’(x) = 0


=


= x2 – 4 = 0


= x =


= x = 2, – 2


At x = 2 f ’(x) changes from –ve to + ve


Since, x = 2 is a point of Minima


Hence, local min value f (2) = 2


More from this chapter

All 137 →
12

Find the points of local maxima or local minima, if any, of the following functions, using the first derivative test. Also, find the local maximum or local minimum values, as the case may be:

 13

Find the points of local maxima or local minima, if any, of the following functions, using the first derivative test. Also, find the local maximum or local minimum values, as the case may be:

f(x) = x3(2x – 1)3

 1

Find the points of local maxima or local minima and corresponding local maximum and local minimum values of each of the following functions. Also, find the points of inflection, if any:

f(x) = x4 – 62x2 + 120x + 9

 1

Find the points of local maxima or local minima and corresponding local maximum and local minimum values of each of the following functions. Also, find the points of inflection, if any:

f(x) = x3 – 6x2 + 9x + 15