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

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 Multiple Choice QuestionsLong 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

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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


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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



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 Multiple Choice QuestionsShort Answer Type

254.

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

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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.
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256. Find all points of local maxima and local minima of the function f given by f (x) = x3  3x + 3.
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257. Find all the points of local maxima and local minima of the function f given by f (x) = 2x3 – 6x2 + 6x + 5 .
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258.

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


f (x) = 3 + | x |, x ∊ R
f is not differentiable at x = 0
∴  0 is a critical point of f.
Now,                 straight f left parenthesis straight x right parenthesis space equals space open curly brackets table attributes columnalign left end attributes row cell 3 minus straight x comma space space space space space space space space space straight x less than 0 end cell row cell 3 plus straight x comma space space space space space space space space space straight x greater than 0 end cell end table close
therefore space space space space straight f apostrophe left parenthesis straight x right parenthesis space equals space open curly brackets table attributes columnalign left end attributes row cell negative 1 comma space space space space space space space space space straight x less than 0 end cell row cell 1 space space space space space space space space space space space space space space straight x greater than 0 end cell end table close
therefore space space space space at space space space straight x space equals space 0 comma space space space space space space space straight f space apostrophe left parenthesis straight x right parenthesis space changes space from space minus ve space to space plus ve
therefore space space space space space space straight x space equals space 0 space is space straight a space point space of space local space minima space of space straight f space and space local space minimum space value space of space straight f space equals space straight f left parenthesis 0 right parenthesis space equals space 3

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259.

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

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260.

What is the maximum value of the function sin x + cos x?

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