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 if f’(x) = x - 1, the equation of the curve y = f(x) passing through the point (1,0) is given by
  • a)
    y=x2 - 2x + 1
  • b)
    y= x2/2 - x + 1/2
  • c)
    y= x2/2 - x + 1
  • d)
    none of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
if f’(x) = x - 1, the equation of the curve y = f(x) passing thr...
Solution:
Given, f(x) = x - 1 and the curve passes through (1,0)

Let's substitute the value of f(x) in the equation of the curve:
y = f(x)
y = x - 1

Substituting (1,0) in the above equation, we get:
0 = 1 - 1
0 = 0

Hence, the point (1,0) satisfies the equation of the curve.

Now, we need to find the equation of the curve.
We can use the method of completing the square to find the equation of the curve.

y = x - 1
y + 1 = x - 1 + 1 (adding 1 on both sides)
y + 1 = x
y = x - 1 (subtracting 1 on both sides)

The equation of the curve is y = x - 1, which is equivalent to option B.

Therefore, the correct answer is option B.

Note: The other options do not satisfy the given conditions.
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