F a function f -2 a - 2 a - - R is an odd function such that f 2 a - x - f x - - x - a - 2 a - and left hand derivative at x - a is 0 then find left handderivative at x-aA- 0 B- 1C- 1-2D- a

The correct option is A f'( a^ )=Lth→0f( a) f( a h)/h Lth→0 f(a)+f(a+h)/h=Lth→0 f(a)+f(a+h)/h=0 ...

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Byju's Answer

Standard XII

Mathematics

Integration as Antiderivative

f a function ...

Question

f a function $f : [- 2 a, 2 a] \to R$ is an odd function such that $f (2 a - x) = f (x), \forall x ϵ [a, 2 a]$ and left hand derivative at x = a is 0 then find left hand derivative at x = -a

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Solution

The correct option is A
$f^{'} (- a^{-}) = L t h \to 0 \frac{f (- a) - f (- a - h)}{h} L t h \to 0 \frac{- f (a) + f (a + h)}{h} = L t h \to 0 \frac{- f (a) + f (a + h)}{h} = 0$

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Similar questions

Left hand derivative and right hand derivative of a function

f (x)

at a point

x = a

are defined as

f^{'} (a^{-}) = lim h \to 0^{+} \frac{f (a) - f (a - h)}{h} = lim h \to 0^{-} \frac{f (a) - f (a - h)}{h} = lim x \to a^{+} \frac{f (a) - f (x)}{a - x}

respectively

Let

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be a twice differentiable function. We also know that derivative of an even function is odd function and derivative of an odd function is even function.

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Left hand derivative and right hand derivative of a function

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at a point

x = a

are defined as

f^{'} (a^{-}) = lim h \to 0^{+} \frac{f (a) - f (a - h)}{h} = lim h \to 0^{-} \frac{f (a) - f (a - h)}{h} = lim x \to a^{+} \frac{f (a) - f (x)}{a - x}

respectively

Let

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The statement

lim h \to 0 \frac{f (- x) - f (- x - h)}{h} = lim h \to 0 \frac{f (x) - f (x - h)}{- h}

implies that for all x

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Left hand derivative and right hand derivative of a function

f (x)

at a point

x = a

are defined as

f^{'} (a^{-}) = lim h \to 0^{+} \frac{f (a) - f (a - h)}{h} = lim h \to 0^{-} \frac{f (a) - f (a - h)}{h} = lim x \to a^{+} \frac{f (a) - f (x)}{a - x}

respectively

Let

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f

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Q. Suppose the quadratic function

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

is such that

f (- 2) = 0 a n d \frac{- b}{2 a} = 1

. Solve

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f a function f:[−2a,2a]→R is an odd function such that f(2a−x)=f(x),∀xϵ[a,2a] and left hand derivative at x = a is 0 then find left hand derivative at x = -a

The correct option is A f′(−a−)=Lth→0f(−a)−f(−a−h)hLth→0−f(a)+f(a+h)h=Lth→0−f(a)+f(a+h)h=0

f a function $f : [- 2 a, 2 a] \to R$ is an odd function such that $f (2 a - x) = f (x), \forall x ϵ [a, 2 a]$ and left hand derivative at x = a is 0 then find left hand derivative at x = -a

The correct option is A
$f^{'} (- a^{-}) = L t h \to 0 \frac{f (- a) - f (- a - h)}{h} L t h \to 0 \frac{- f (a) + f (a + h)}{h} = L t h \to 0 \frac{- f (a) + f (a + h)}{h} = 0$