If f (x) = min { 1, $x^2, x^3$ }, then
- f (x) is continuous everywhere
- f (x) is continuous and differentiable everywhere
- f (x) is not differentiable at two points
- f (x) is not differentiable at one point
The Correct Option is D
Solution and Explanation
The correct option are(A and D): f (x) is continuous everywhere and f (x) is not differentiable at one point.
Here, f (x) = min { 1, \(x^2, x^3\) } which could be graphically
shown as
\(\Rightarrow\) f (x) is continuous for x \(\in\) R and not differentiable at
x = 1 due to sharp edge.
Hence, (a) and (d) are correct answers.
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Concepts Used:
Maxima and Minima
What are Maxima and Minima of a Function?
The extrema of a function are very well known as Maxima and minima. Maxima is the maximum and minima is the minimum value of a function within the given set of ranges.
There are two types of maxima and minima that exist in a function, such as:
- Local Maxima and Minima
- Absolute or Global Maxima and Minima