Which of the following points lies on the tangent to the curve at the point ?
Explanation for the correct option:
The slope of the tangent to the curve is given as .
Step 1: Find the derivative of the given equation of the curve.
Step 2: Put the point in the derivative.
Step 3: Derive the equation of tangent.
We know that the equation of the tangent to any curve is given by
The equation of the tangent
Step 4: Put in the equation of tangent.
Since the left-hand side is equal to the right-hand side, is the point that lies on the tangent to the curve.
Hence, the correct answer is option C
Explanation of incorrect option:
Option (A)
Put in the equation of tangent.
Since the left-hand side is not equal to the right-hand side, is not a point that lies on the tangent to the curve.
Option(B)
Put in the equation of tangent.
Since the left-hand side is not equal to the right-hand side, is not a point that lies on the tangent to the curve.
Option(D)
Put in the equation of tangent.
Since the left-hand side is not equal to the right-hand side, is not a point that lies on the tangent to the curve.
So, the options A, B, and D are incorrect.
Hence, the correct answer is option C.