Question

The equation of the tangent at the point (2,3) on the curve y= ax^3+b Is y=4x-5 then the value of a&b is

Answer 1

Answer:

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Step-by-step explanation:

The equation of the curves is y2=ax2+b....(1)

Differentiable the equation of curve wrt x

2ydxdy=3ax2

dxdy=2y3ax2

At point (2,3)

(dxdy)2,3=2(3)3a(1)

(dxdy)2,3=2a

The equation of tangent at point (2,3) is

(y−5)=2a(x−2)

⇒y=2ax−4x+3....(3)

But in the given question the line touches the curve at (2,1) is y=4x−5...(3)

which is tangent to the curve in the equation represent the same line new comparing the represents of both the lines 

2a4⇒a=2

3−4a=−5⇒a=2

Moreover, the point (2,3) lies on the curve y2=ax3+b so

(3)2=a(2)3+b

9=8a+b

9=8×

Hence, the values of a and b are 2 and −7, respectively.