Question

Let f (x) = Ï•(x) + ψ(x) and Ï•(a), ψ’(a) are finite and definite. Then:

Solution

Correct option is

f (x) is continuous at x = a & f (x) is differentiable at x = a

We know that the sum of two continuous (differentiable) functions is continuous (differentiable). 

∴  f (x) is continuous and differentiable at x = a.

 

SIMILAR QUESTIONS

Q1

The function f (x) = (x2 – 1) |x2 – 3x +2| + cos ( | | ) is not differentiable at

Q2
Q3

The number of points in (1, 3), where is not differentiable is:

Q4

Let f and g be differentiable function satisfying g’ (a) = 2, g (a) = b and fog = I (identity function) Then, f’(b) is equal to:

Q5

If the function , (where [.] denotes the greatest integer function) is continuous and differentiable in (4, 6), then.

Q6

Let [.] denotes the greatest integer function and f (x) = [tan2x], then:

Q7

Let f be a real function satisfying f (x + z) = f (xf (yf (zfor all real xyz . If f (2) = 4 and f’ (0) = 3. Then find f (0) and f’ (2).

Q8

Let h(x) = min.{xx2} for every real number of x. Then:

Q9

Let f : R → R be a function defined by f (x) =  max. {xx3}. The set of all points where (x) is not differentiable is:

Q10

If f (x) = x + tan and g(x) is the inverse of f (x) then g’ (x) is equal to: