Related InterviewSolutions

• Write an example of a function which is everywhere continuous but fails to be differentiable exactly at five points.
• It is given that f'(a) exists, then \(\lim\limits_{x \to a} \frac{xf(a)-af(x)}{x-a}\) is …(a) f(a) – af'(a) (b) f ‘(a) (c) -f ‘(a) (d) f(a) + af ‘(a)
• The derivative of f(x) = x|x| at x = -3 is …(a) 6 (b) -6 (c) does not exist (d) 0
• If f(x) = x + 2, then f'(f(x)) at x = 4 is …(a) 8 (b) 1 (c) 4 (d) 5
• If y = mx + c and f(0) = f'(0) = 1, then f(2) is …(a) 1 (b) 2 (c) 3 (d) -3
• Find the derivatives of the function with respect to corresponding independent variables.y = ex sin x
• Find the derivatives of the function with respect to corresponding independent variables.(i) y = cos x – 2 tan x(ii) g(t) = t3 cos t
• Find the derivatives of the function with respect to corresponding independent variables.g(t) = 4 sec t + tan t
• Find the derivatives of the function with respect to corresponding independent variables.(i) y = sin x + cos x(ii) f(x) = x sin x
• Find the derivatives of the function with respect to corresponding independent variables. f(x) = x – 3 sin x