Maths-
General
Easy
Question
Suppose that
is differentiable for allx and that
for all x If
and f(4)=8 then f(2) has the value equal to
- 8
The correct answer is: ![4](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAANCAYAAACQN/8FAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAE5JREFUeNpjYMAOfID4PwMBwAPE14hROBOIkwkptAbivVA2ToVsQHwJiOUJKewA4hwkPlaFekB8FE0Mq8KTQKxCjML/BDBeQFAB7RSiAADJqxnbA8YC5wAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW4+NDwvbW4+PC9tYXRoPhlZrqYAAAAASUVORK5CYII=)
In the question it is given that f is differentiable to solve lets use Lagranges mean value theorem innn the interval [1,4]
f'(c)= f(4)-f(1)/3
f'(c)=2
f'(x)=2
f(x)=2x+4
f(1)=2+k
k=0
f(x)=2x
f(2)=4
Hence f(2)=4 is the suitable option
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in the above fig,
.![text end text left floor text d end text](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAQCAYAAAAWGF8bAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAAHNJREFUeNpjYMAO/jNQGQy4gf+Ht4H2QHwBiH8B8V0gTqTEQA0gvgbEOlC+FhCvocTAuUAcSU0vPwdiDmoa+IfakfIDiJmoaeB+ILZGExOmxEBzIN4NxNJQl/oA8VFK06EaEG+Aeh9kmAEtcgpRWQkZEw0ATgMt9IemvzkAAAB1dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG10ZXh0PiYjeEEwOzwvbXRleHQ+PG1vPiYjeDIzMEE7PC9tbz48bXRleHQ+ZDwvbXRleHQ+PC9tYXRoPp+lmPMAAAAASUVORK5CYII=)
in the above fig,
.![text end text left floor text d end text](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAQCAYAAAAWGF8bAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAAHNJREFUeNpjYMAO/jNQGQy4gf+Ht4H2QHwBiH8B8V0gTqTEQA0gvgbEOlC+FhCvocTAuUAcSU0vPwdiDmoa+IfakfIDiJmoaeB+ILZGExOmxEBzIN4NxNJQl/oA8VFK06EaEG+Aeh9kmAEtcgpRWQkZEw0ATgMt9IemvzkAAAB1dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG10ZXh0PiYjeEEwOzwvbXRleHQ+PG1vPiYjeDIzMEE7PC9tbz48bXRleHQ+ZDwvbXRleHQ+PC9tYXRoPp+lmPMAAAAASUVORK5CYII=)
physics-General
physics-
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physics-
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physics-General
physics-
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physics-General
physics-
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physics-
The total potential difference = ...... volt
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physics-General
physics-
![](data:image/png;base64,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)
The total p.d = .................. volt
![](data:image/png;base64,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)
The total p.d = .................. volt
physics-General
physics-
The total p.d = ..................... volt
The total p.d = ..................... volt
physics-General
physics-
Find the effective P. d
Find the effective P. d
physics-General
physics-
physics-General