Show that f(x) = |x - 3| is continuous but not differentiable at x = 3.

Show that f(x) = is not differentiable at x = 0.

Show that the function f defined as follows,

Is continuous at x = 2, but not differentiable there at x = 2.

Discuss the continuity and differentiability of f(x) = |x| + |x - 1| in the interval ( - 1,2).

Find whether the following function is differentiable at x = 1and x= 2 or not:

f(x) =

Show that the function F(x) = is

Differentiable at x = 0, if m > 1.

Show that the function F(x) = is

Continuous but not differentiable at x = 0, if 0<m<1.

Show that the function F(x) = is

Neither continuous and nor differentiable, if m≤0.

Find the values of a and b so that the function

f(x) =

is differentiable at each x € R.

Show that the function

F(x) =

Is continuous but not differentiable at x = 1.

If is differentiable at x = 1, find a and b.

Find the values of a and b, if the function f(x) defined by

is differentiable at x = 1.

If f is defined by f (x) = x², find f ‘ (2).

Show that the derivative of the function f given by f (x) = 2x³ – 9x² + 12x + 9, at x = 1 and x = 2 are equal.

If for the function Φ (x) = λx² + 7x – 4, Φ’ (5) = 97, find λ.

If f (x) = x³ + 7x² + 8x – 9, find f ‘ (4).

Find the derivative of the function f defined by f (x) = mx + c at x = 0.

Examine the differentiability of the function f defined by

Write an example of a function which is everywhere continuous but fails to be differentiable exactly at five points.

Discuss the continuity and differentiability of f (x) = |log |x| |.

Discuss the continuity and differentiability of f (x) = e ^|x|.

Discuss the continuity and differentiability of

Is |sin x| differentiable? What about cos |x|?

Define differentiability of a function at a point.

Is every differentiable function continuous?

Is every continuous function differentiable?

Give an example of a function which is continuous but not differentiable at a point.

If f(x) is differentiable at x = c, then write the value of .

If f(x) = |x – 2| write whether f’ (2) exists or not.

Write the points where f(x) = |log_e x| is not differentiable.

Write the points of non-differentiability of f(x) = |log|x||.

Write the derivative of f(x) = |x|³ at x = 0.

Write the number of points where f(x) = |x| + |x – 1| is continuous but not differentiable.

Write the value of the derivative of f(x) = |x – 1| + |x – 3| at x = 2.

If write the value of

Choose the correct answer.

Let f(x) = |x| and g(x) = |x³|, then

Choose the correct answer.

The function f(x) = sin^–1(cos x) is

Choose the correct answer.

The set of points where the function f(x) = x|x| is differentiable is

Choose the correct answer.

If then f(x) is

Choose the correct answer.

Let f(x) = (x + |x|) |x|. Then, for all x

Choose the correct answer.

The function f(x) = e^–|x| is

Choose the correct answer.

The function f(x) = |cos x| is

Choose the correct answer.

If then f(x) is

Choose the correct answer.

If f(x) = a |sinx| + b e^|x| + c|x³| and if f(x) is differentiable at x = 0, then

Choose the correct answer.

If then at x = 0, f(x)

Choose the correct answer.

If f(x) = |log_e x|, then

Choose the correct answer.

f(x) = |log_e |x||, then

Choose the correct answer.

Let If f(x) is continuous and differentiable at any point, then

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The function f(x) = x – [x], where [.] denotes the greatest integer function is

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Let Then, f(x) is derivable at x = 1, is

Choose the correct answer.

Let f(x) = |sin x|. Then,

Choose the correct answer.

Let f(x) = |cos x|. Then,

Choose the correct answer.

The function f(x) = 1 + |cos x| is

Choose the correct answer.

The function f(x) = |cos x| is

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The function where [.] denotes the greatest integer function, is

Choose the correct answer.

Let f(x) = a + b |x| + c |x|⁴, where a, b, and c are real constants. Then, f(x) is differentiable at x = 0, if

Choose the correct answer.

If f(x) = |3 – x| + (3 + x), where (x) denotes the least integer greater than or equal to x, then f(x) is

Choose the correct answer.

If then f(x) is

Choose the correct answer.

If then at x = 0, f(x) is

Choose the correct answer.

The set of points where the function f(x) given by f(x) = |x – 3| cos x is differential then,

Choose the correct answer.

Let Then, f is