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Modulus Function

If f x = ex...

Question

If $f (x) = e^{x^{2} - 4 x + 3}$ on $[- 5, 5]$ then log (greatest value of $f (x)$ ) is

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Solution

$f (x) = e^{x^{2} - 4 x + 3} f^{'} (x) = {(e}^{x^{2} - 4 x + 3}) . (2 x - 4) f^{''} (x) = {(e}^{x^{2} - 4 x + 3}) .2 f^{'} (x) i s 0 a t x = 2 a n d f^{''} (x) i s a l w a y s p o s i t i v e . s o a t x = 2 f (x) i s m i n i m u m . a n d x = [- 5, 5] t h a t m e a n s t h a t f (x) i s d e c r e a s i n g f r o m [- 5, 2] a n d a f t e r t h a t i t i s i n c r e a s i n g t i l l x = 5. s o f (- 5) = e^{48} a n d f (5) = e^{8} s o f (x) w o u l d b e m a x . a t x = - 5 a n d log (g r e a t e s t v a l u e o f f (x)) = log (e^{48}) = 48.$

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Similar questions

f (x) = x^{2} log x

[1, e]

then log (greatest of

f (x)

f (x)

f (x) = \frac{4^{x}}{4^{x} + 2}

, then the value of

f (x) + f (1 - x)

f (x) = a - {(x - 3)}^{89}

, then greatest value of f(x) is

f (x)

be a function satisfying

f^{'} (x) = \frac{x^{3} - f (x)}{x} w i t h f (2) = 2

then the value of

(\int_{1}^{2} e^{x^{2}} . f (x) d x)

f (x) = \frac{e^{x^{2}} - cos x}{x^{2}}

x \neq 0

is continuous at

x = 0

, then value of

f (0)

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