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CBSE Class 12-science Answered

Q) Let y=f(x) , f colon R rightwards arrow R space b e space a n space o d d space d i f f e r e n t i a b l e space f u n c t i o n space s u c h space t h a t space f apostrophe apostrophe apostrophe left parenthesis x right parenthesis greater than 0 space & space g left parenthesis alpha comma beta right parenthesis equals sin to the power of 8 alpha plus cos to the power of 8 beta plus 2 minus 4 sin squared alpha cos squared beta. I f space f " left parenthesis g left parenthesis alpha comma beta right parenthesis right parenthesis equals 0 comma space t h e n space space p r o v e space t h a t space sin squared alpha plus sin squared beta space i s space e q u a l space t o space 1.
Asked by araima2001 | 02 Jul, 2017, 02:38: AM
answered-by-expert Expert Answer
begin mathsize 16px style Odd space differential space function space means function space is space odd straight f apostrophe left parenthesis straight x right parenthesis equals fraction numerator df left parenthesis straight x right parenthesis over denominator dx end fraction equals fraction numerator straight d open parentheses negative straight f left parenthesis negative straight x right parenthesis close parentheses over denominator dx end fraction equals negative fraction numerator straight d open parentheses straight f left parenthesis negative straight x right parenthesis close parentheses over denominator dx end fraction equals negative open parentheses negative straight f apostrophe open parentheses negative straight x close parentheses close parentheses equals straight f apostrophe open parentheses negative straight x close parentheses Use space this space and space second space derivative space test space to space prove space it end style
Answered by Sneha shidid | 04 Jul, 2017, 10:57: AM

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CBSE 12-science - Maths
Find the local maxima and local minima for the given function and also find the local maximum and local minimum values f(x)=x99, xf(-3,3)
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CBSE 12-science - Maths
Fimd the point of local maxima and local minima and corresponding local maxima and local minima values of each of the following funct. F(x) = x^3 -2ax^2 a^2x, a>0 ,x belongs to real no.
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CBSE 12-science - Maths
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CBSE 12-science - Maths
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CBSE 12-science - Maths
Show that the volume of largest cone that can be inscribed in a sphere of radius R is 8 over 27 of the volume of the sphere.
Asked by Topperlearning User | 21 Aug, 2014, 01:22: PM
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CBSE 12-science - Maths
Show that the rectangle of maximum area that can be inscribed in a circle of radius r is a square of side square root of 2 straight r
Asked by Topperlearning User | 19 Aug, 2014, 09:25: AM
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CBSE 12-science - Maths
A square piece of tin of side 18 cm is to made into a box without top by cutting a square from each corner and folding up the flaps to form a box. What should be the side of the square to be cut off so that the volume of the box is maximum. On four sides of this box, write four life skills.
Asked by Topperlearning User | 21 Aug, 2014, 12:21: PM
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CBSE 12-science - Maths
Suppose a company manufactures x units. And the cost of manufacturing these x units comes out to be a cost function given as c(x)=2x3 -60x2 +1500. Definitely the company would like to minimise its cost to attain maximum profit. So here we would like to know how many units should be manufactured to get minimum cost,
Asked by Topperlearning User | 19 Aug, 2014, 08:45: AM
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CBSE 12-science - Maths
Suppose a certain sheet of metal is given and we need to make a right circular cylinder tin out of it such that it contains maximum quantity of oil. Here we assume no metal is wasted.
Asked by Topperlearning User | 19 Aug, 2014, 09:12: AM
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CBSE 12-science - Maths
A window is in the form of a rectangle surmounted by a semi circular opening. The total perimeter of the window is 10 m. Find the dimensions o the window to admit maximum light through the whole opening. Do you think that by getting maximum light, we can save electricity? Do you agree that we should save electricity?
Asked by Topperlearning User | 19 Aug, 2014, 09:38: AM
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