Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

f(x) =  (x \[-\] 1) (x+2)². 

f(x) = \[\frac{1}{x^2 + 2}\] .

f(x) =  x³ \[-\] 6x² + 9x + 15 . 

f(x) = sin 2x, 0 < x < \[\pi\] .

f(x) =  sin x \[-\] cos x, 0 < x < 2\[\pi\] .

f(x) =  cos x, 0 < x < \[\pi\] .

`f(x)=sin2x-x, -pi/2<=x<=pi/2`

`f(x)=2sinx-x, -pi/2<=x<=pi/2`

f(x) =\[x\sqrt{1 - x} , x > 0\].

Find the point of local maximum or local minimum, if any, of the following function, using the first derivative test. Also, find the local maximum or local minimum value, as the case may be:

f(x) = x³(2x \[-\] 1)³.

f(x) =\[\frac{x}{2} + \frac{2}{x} , x > 0\] .

Find the projection of \[\vec{b} + \vec{c}  \text { on }\vec{a}\]  where \[\vec{a} = 2 \hat{i} - 2 \hat{j} + \hat{k} , \vec{b} = \hat{i} + 2 \hat{j} - 2 \hat{k} \text{ and } \vec{c} = 2 \hat{i} - \hat{j} + 4 \hat{k} .\]

If \[\vec{a} = 5 \hat{i} - \hat{j} - 3 \hat{k} \text{ and } \vec{b} = \hat{i} + 3 \hat{j} - 5 \hat{k} ,\] then show that the vectors \[\vec{a} + \vec{b} \text{ and } \vec{a} - \vec{b} \] are orthogonal.

f(x) = x⁴ \[-\] 62x² + 120x + 9.

f(x) = x³\[-\] 6x² + 9x + 15

f(x) = (x - 1) (x + 2)².

`f(x) = 2/x - 2/x^2,  x>0`

f(x) = xe^x.

`f(x) = x/2+2/x, x>0 `.

`f(x) = (x+1) (x+2)^(1/3), x>=-2` .