Jamia Millia Islamia Differentibility Previous Year Questions (PYQs)
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Showing 4 questions
. Find the number of points where
$f(x) = |2x + 1| - 3|x + 2| + |x^2 + x - 2|$
is non-differentiable.
1
2
3
4
Solution
**Solution:**
Non-differentiable points occur where expressions inside modulus = 0.
1. $2x + 1 = 0 \Rightarrow x = -\dfrac{1}{2}$
2. $x + 2 = 0 \Rightarrow x = -2$
3. $x^2 + x - 2 = 0 \Rightarrow x = 1, -2$
Unique points: $x = -2, -\dfrac{1}{2}, 1$
Hence, number of non-differentiable points = 3.
$\boxed{\text{Answer: (B) 3}}$
Which of the following functions show that the statement
"If a function is continuous at $x=0$, then it is differentiable at $x=0$" is false?
1
2
3
4
Solution
$f(x) = x^{1/3}$ is continuous at $x = 0$ but derivative $\dfrac{df}{dx} = \dfrac{1}{3}x^{-2/3}$
is not defined at $x = 0.$
Hence, function is continuous but not differentiable at 0.
Number of points at which the function $f(x) = \min(|x|, |x+1|, |x-4|)$
is not differentiable is:
1
2
3
4
Solution
Each $|x|$ term is non-differentiable at the point where its argument = 0.
Points: $x = 0, -1, 4$.
If $f(x) = \max{x,,x^3}$, number of points where $f(x)$ is not differentiable are
1
2
3
4
Solution
$x=x^3$ → $x=0,\pm1$.
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