Question

In the diagram, the tangent to the curve y = f(x) = ax²-3x + b at A(2; 3) meets the x-axis at B(1; 0). The line perpendicular to the tangent at A meets the x-axis at C. A(2,3) B(1:0) C find a and b

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Answer 1

a= 9/8

b= 21/2

The slop of the tangent line is 2ax-3 which is the derivative of the curve.

there are two points on the tangent line which are (2,3) & (1,0), so the slope of the tangent will be 3/2. solving for a we get 9/8 then solving for b we get 21/2