Trying to find the right answer to this..

Name: Zigya - For The Curious Learner
Rating: 4.4 (740 reviews)

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Application of Derivatives

Long Answer Type

251. Find the local maxima or local minima, if any, of following functions using the first derivative test only. Find also the local maximum and the local minimum values, as the case may be:

straight x cubed left parenthesis straight x minus 1 right parenthesis squared

71 Views

252. Find the local maxima or local minima, if any, of following functions using the first derivative test only. Find also the local maximum and the local minimum values, as the case may be:

straight x cubed left parenthesis 2 straight x minus 1 right parenthesis cubed

72 Views

253. Find the local maxima or local minima, if any, of following functions using the first derivative test only. Find also the local maximum and the local minimum values, as the case may be:

negative left parenthesis straight x minus 1 right parenthesis cubed space left parenthesis straight x plus 1 right parenthesis squared

81 Views

Short Answer Type

254.

Find all the local maxima or minima of the function
f (x) = x³– 12x.

88 Views

255. Find all the points of local maxima and local minima of the function f given by f (x) = x³ – 27 x + 3. Also, find local maximum and local minimum value of f.

86 Views

256. Find all points of local maxima and local minima of the function f given by f (x) = x³– 3x + 3.

91 Views

257. Find all the points of local maxima and local minima of the function f given by f (x) = 2x³ – 6x² + 6x + 5 .

91 Views

258.

Find local minimum value of the function f given by f(x) = 3+ | x |, x ∊ R.

74 Views

259.
Find local maximum and local minimum values of the function f given by
f (a) = 3x⁴ + 4x³ – 12x² + 12

f (x) = 3 x⁴+ 4 x³– 12 x²+ 12
f ' (x) = 12 x³+ 12 x²– 24 x = 12 x (x² + x – 2)
f ' (x) = 12 x (x – 1) (x + 2)
f ' (x) = 0 ⇒ 12 a (x – 1) (x + 2) = 0
∴ x = 0, 1, – 2
f ' (x) = 36 x² + 24 x – 24
At x = 0, f ' (x) = 0 + 0 24 = – 24 < 0
∴ x = 0 is a point of local maximum
and local maximum value = 0 + 0 – 0 + 12 = 12
At x = 1, f ' (x) = 36 + 24 – 24 = 36 > 0
∴ x = 1 is a point of local minima
and local minimum value = 3+ 4 – 12 + 12 = 7
At x = – 2, f ' (x) = 36 (4) + 24 (– 2) – 24 = 72 > 0
∴ x = – 2 is a point of local minima
and local minimum value = 3 (–2)⁴ + 4 (–2)³ – 12(–2)² + 12
= 3 (16) + 4 (– 8) – 12 (4) + 12 = 48– 32 – 48 + 12 = – 20