JEE Advanced Mathematics: Calculus (Differentiation) Practice Questions

7 questions with answers and step-by-step solutions. Tap any question to see the full worked solution.

Q1.
$Let f(x) = |x - 1| + |x - 2| + |x - 3|. The number of points where f(x) is not differentiable is:$
Medium
Q2.
$L e t f (x) = e^{x} + x . I f g (x) i s t h e in v er se f u n c t i o n o f f (x), t h e n g^{'} (1) i s :$
Medium
Q3.
$Let f(x) be a differentiable function such that f(x + y) = f(x) + f(y) + xy(x + y) for all real x and y, and f'(0) = 1. Find the value of f'(1).$
Medium
Q4.
$If y = x^x^x^... to infinity, then dy/dx is equal to:$
Medium
Q5.
$I f y = (s in x)^{(} t an x), f in dd y / d x a t x = p i /4.$
Hard
Q6.
$Let f(x) = |x-1| + |x-2|. Find the number of points where f(x) is not differentiable.$
Hard
Q7.
$L e t f (x) = in t e g r a l f r o m 0 t o x o f (e^{t} / (1 + t)) d t . F in d f^{''} (0) .$
Hard

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