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Formation of a Differential Equation from a General Solution

State the fol...

Question

State the following statement is True or False
Slope of a tangent at any point changes when we shift the function $f (x)$ to $f (x) \pm a$ .

True

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False

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Solution

The correct option is B False
Slope of any point remains unchanged even though the function is shifted upwards or downwards. Thus the given statement is false.

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f (x) - a

f (x)

a

State the following statement is True or False

$f (x) + a$ is $f (x)$ shifted upward by $a$ units.

1

0

f (x)

P

P

f (x) = a x^{2} + b x + c

a > 0

y = f (x)

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(x, f (x))

f (x) + x f^{'} (x) = x^{2}

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