Answer: \(a=3\), \(b=-10\).

Answer: \(a=3\), \(b=-10\).

Differentiate the curve:

\(\frac{dy}{dx}=2ax-5.\)

At \(x=2\), the gradient of the tangent is \(7\), so

\(4a-5=7.\)

Thus

\(4a=12,\qquad a=3.\)

The curve is therefore

\(y=3x^2-5x+2.\)

At \(x=2\),

\(y=3(2)^2-5(2)+2=12-10+2=4.\)

The tangent \(y=7x+b\) passes through \((2,4)\), so

\(4=7(2)+b.\)

Hence

\(b=-10.\)