HSC Arts इयत्ता ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions

Find the derivatives of the following functions using first principle.

f(x) = 6

Find the derivatives of the following functions using first principle.

f(x) = – 4x + 7

Find the derivatives of the following functions using first principle.

f(x) = – x² + 2

Find the derivatives from the left and from the right at x = 1 (if they exist) of the following functions. Are the functions differentiable at x = 1?

`f(x) = |x - 1|`

Find the derivatives from the left and from the right at x = 1 (if they exist) of the following functions. Are the functions differentiable at x = 1?

`f(x) = sqrt(1 - x^2)`

Find the derivatives from the left and from the right at x = 1 (if they exist) of the following functions. Are the functions differentiable at x = 1?

`f(x) = {{:(x",", x ≤ 1),(x^2",", x > 1):}`

Determine whether the following function is differentiable at the indicated values.

f(x) = x |x| at x = 0

Determine whether the following function is differentiable at the indicated values.

f(x) = |x² – 1| at x = 1

Determine whether the following function is differentiable at the indicated values.

f(x) = |x| + |x – 1| at x = 0, 1

Determine whether the following function is differentiable at the indicated values.

f(x) = sin |x| at x = 0

Show that the following functions are not differentiable at the indicated value of x.

`f(x) = {{:(-x + 2, x ≤ 2),(2x - 4, x > 2):}` , x = 2

Show that the following functions are not differentiable at the indicated value of x.

`f(x) = {{:(3x",", x < 0),(-4x",", x ≥ 0):}` , x = 0

The graph of f is shown below. State with reasons that x values (the numbers), at which f is not differentiable.

If f(x) = |x + 100| + x², test whether f’(–100) exists.

Examine the differentiability of functions in R by drawing the diagram

|sin x|

Examine the differentiability of functions in R by drawing the diagram

|cos x|

Choose the correct alternative:

f y = f(x² + 2) and f'(3) = 5 , then `("d"y)/("d"x)` at x = 1 is

Choose the correct alternative:

If f(x) = x² – 3x, then the points at which f(x) = f’(x) are

Choose the correct alternative:

If y = mx + c and f(0) = f’(0) = 1, then f(2) is

Choose the correct alternative:

If f(x) = x + 2, then f'(f(x)) at x = 4 is