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If dy/dx = (x - a)2n (x - b)2p + 1, where n and p are positive integers, then at x = a, x = b, f(x) has respectively :
- a)neither maxima nor minima, minima
- b)minima, maxima
- c)minima, neither maxima nor minima
- d)maxima, minima
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If dy/dx = (x - a)2n (x - b)2p + 1,wherenandpare positive integers, th...
For stationary points, put dy/dx = 0
i.e. (x – a)2n(x – b)2p+1 = 0
i.e. x = a, b
Nature at x = a : Since 2n is even, dy/dx does not change its sign while x passes through a.
i.e. (x – a)2n(x – b)2p+1 = 0
i.e. x = a, b
Nature at x = a : Since 2n is even, dy/dx does not change its sign while x passes through a.
∴ Neither maximum nor minima at x = a.
Nature at x = b : when x is slightly less than 
is negative as 2p + 1 is odd.
is negative as 2p + 1 is odd.Also, when x is slightly more than 
is positive. Thus, y is minimum at x = b.
is positive. Thus, y is minimum at x = b.The correct answer is: neither maxima nor minima, minima
Most Upvoted Answer
If dy/dx = (x - a)2n (x - b)2p + 1,wherenandpare positive integers, th...
Explanation:
At x = a:
- When x = a, the expression becomes (a - a)^2n (a - b)^2p + 1 = 0^2n (a - b)^2p + 1 = 1.
- This implies that at x = a, the function f(x) has neither maxima nor minima.
At x = b:
- When x = b, the expression becomes (b - a)^2n (b - b)^2p + 1 = (b - a)^2n * 0^2p + 1 = 1.
- This implies that at x = b, the function f(x) has neither maxima nor minima.
Therefore, the correct answer is option 'A' - neither maxima nor minima at x = a and x = b.
At x = a:
- When x = a, the expression becomes (a - a)^2n (a - b)^2p + 1 = 0^2n (a - b)^2p + 1 = 1.
- This implies that at x = a, the function f(x) has neither maxima nor minima.
At x = b:
- When x = b, the expression becomes (b - a)^2n (b - b)^2p + 1 = (b - a)^2n * 0^2p + 1 = 1.
- This implies that at x = b, the function f(x) has neither maxima nor minima.
Therefore, the correct answer is option 'A' - neither maxima nor minima at x = a and x = b.
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If dy/dx = (x - a)2n (x - b)2p + 1,wherenandpare positive integers, then atx=a,x=b,f(x)has respectively :a)neither maxima nor minima, minimab)minima, maximac)minima, neither maxima nor minimad)maxima, minimaCorrect answer is option 'A'. Can you explain this answer?
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