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Discuss the differentiability of {f{{({x})}}}={|{({})}_{{e}}|}

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Discuss the differentiability of $f (x) = ∣ (lo g)_{e} ∣ x ∣ ∣$

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Discuss the differentiability of

f (x) = ∣ (lo g)_{e} ∣ x ∣ ∣

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Practice questions from similar books

Question 1

f (x) = {[x] + {x}, x < 1 \frac{1}{[ x ] + { x } ^{2}}, x \geq 1

, then [where [.] and {.] represent the greatest integer and fractional part functions respectively]

f (x)

is continuous at

x = 1

f (x)

is not continuous at

x = 1

f (x)

is differentiable at

x = 1

(lim)_{x 1} f (x)

does not exist

View solution

Question 2

f (x) = {sin (\frac{π}{2}) (x - [x]) x 5)

is continuous at

x = 5, a, b \in R

then ([.] denotes the greatest integer function) (A)

a = \frac{25}{108}, b = \frac{6}{5}

(B)

a = \frac{6}{13}, b = \frac{17}{29}

(C)

a = \frac{1}{2}, b = \frac{25}{36}

(D)

a = \frac{23}{100}, b = \frac{6}{5}

View solution

Question 3

f (x) = (tan (\frac{π}{4} + (lo g)_{e} x))^{(l o g)_{x} e}

is to be made continuous at

x = 1,

then what is the value of

f (1) ?

View solution

Question 4

Suppose

f : R R^{+}

be a differentiable function such that

3 f (x + y) = f (x) f (y) \forall x, y \in R

with

f (1) = 6 .

Then the value of

f (2)

6

9

12

15

View solution

Question Text

Discuss the differentiability of

f (x) = ∣ (lo g)_{e} ∣ x ∣ ∣

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Discuss the differentiability of f(x)=∣(log)e​∣x∣∣

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Practice questions from similar books

Discuss the differentiability of $f (x) = ∣ (lo g)_{e} ∣ x ∣ ∣$