Q. 3 E4.4( 5 Votes )
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) = x3 – 6x2 + 9x + 15
Answer :
f (x) = x3 – 6x2 + 9x + 15
⇒ f’(x) = 3x2 – 12x + 9
Now, f’(x) = 0
⇒ 3x2 – 12x + 9 = 0
⇒ 3(x-1)(x-3) = 0
⇒ x = 1,3
g’’(x) = 6x – 12 =6(x-2)
Now, f’(1) = 6(1-2)=-6 < 0
and f’(3) = 6(3-2) = 6 > 0
Then, by second derivative test,
⇒ x = 1 is point of local maxima and local maximum of f at x = 1 is
f(1) = 13 – 6 +9 +15 = 19
And,
x = 3 is point of local minima and local minimum value of f at x = 3 is
f(3) = 27 – 54 + 27 +15 = 15
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
PREVIOUSFind 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) = sin x – cos x, 0 < x < 2πNEXTFind 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:
RELATED QUESTIONS :
Show that the maximum value of 
is 
Mark (√) against the correct answer in the following:
At 
is
RS Aggarwal - Mathematics
Find the point of local maxima or local minima or local minima and the corresponding local maximum and minimum values of each of the following functions:
RS Aggarwal - Mathematics
Find the point of local maxima or local minima or local minima and the corresponding local maximum and minimum values of each of the following functions:
RS Aggarwal - Mathematics
