The equation of tangent at (2, 3) on the curve y2 = ax3 + b is y = 4x – 5. Find the values of a and b.
The equation of the given curve is
Differentiate equation (1) with respect to x, we get
So, equation of tangent at the point (2, 3) is
But according to question,
Equation of tangent at the point (2,3) is y=4x−5
Both the equation represents the same line, therefore comparing the coefficients of both the line, we have
2a=4⇒a=2 and 3−4a=−5⇒a=2 .....(3)
The point (2, 3) lies on the curve y2=ax3+b, so
⇒9=8×2+b [From (3)]
Hence, the values of a and b are 2 and −7, respectively.