A curve passes through the point and the slope of the tangent at any point is for all values of . The point of maximum ordinate on the curve is :
Explanation for the correct option:
Step 1: Find the equation of the curve.
We have been given that, a curve whose slope of the tangent at any point is for all values of .
We need to find the point of maximum ordinate on the curve.
The slope of the tangent be,
To find the equation of curve we integrate the above equation:
Step 2: Find the value of integration constant ‘c’.
Since the curve passes through , equation of the curve would be,
So, the equation of the curve would be,
Step 3: Find the critical point.
We know, to find the critical point,
Step 4: To decide maximum and minimum point find .
Step 5: Find the point of maxima.
This means the curve has the maximum value at .
Step 6: Find the point of maximum ordinate on the curve.
At ,
The required point is
Therefore, option (C) is the correct answer.