Q3 of 168 Page 231

Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be:

f (x) = x2

f(x) = x2

⇒ f’(x) = 2x


Now, f’(x) = 0


⇒ x = 0


⇒ x = 0 is the only critical point which could possibly be the point of local maxima or local minima of f.


⇒ f’’(0) = 2, which is positive.


Then, by second derivative test,


⇒ x = 0 is point of local maxima and local minima of f at x = 0 is f(0) = 0.


More from this chapter

All 168 →
2

Find the maximum and minimum values, if any, of the following functions given by

f (x) = |sin 4x + 3|

 2

Find the maximum and minimum values, if any, of the following functions given by

h(x) = x + 1, x ∈ (–1, 1)

 3

Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be:

g(x) = x3 – 3x

 3

Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: