Advertisements
Advertisements
Question
Examine the differentiability of functions in R by drawing the diagram
|cos x|
Solution
|cos x| = f(x)
Limit exist and continuous for all x ∈ R clearly, differentiable at `"R" {(2"n" + 1)π/2, "n" ∈ "z"}` Not differentiable at x = `(2"n" + 1) π/2`, n ∈ Z.
APPEARS IN
RELATED QUESTIONS
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) = 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) = 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
The graph of f is shown below. State with reasons that x values (the numbers), at which f is not differentiable.
Examine the differentiability of functions in R by drawing the diagram
|sin 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 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
Choose the correct alternative:
If pv = 81, then `"dp"/"dv"` at v = 9 is
Choose the correct alternative:
It is given that f'(a) exists, then `lim_(x -> "a") (xf("a") - "a"f(x))/(x - "a")` is
Choose the correct alternative:
If g(x) = (x2 + 2x + 1) f(x) and f(0) = 5 and `lim_(x -> 0) (f(x) - 5)/x` = 4, then g'(0) is
Choose the correct alternative:
If f(x) = `{{:(x + 2, - 1 < x < 3),(5, x = 3),(8 - x, x > 3):}` , then at x = 3, f'(x) is
