2.77: Cubic curve gradient and tangent

0606/23/O/N/19 — Question 8 · 5 marks

Given that a curve has equation y=x3−x2+bx+24y = x^{3} - x^{2} + bx + 24, find, using your value of bb from earlier parts (b=−14b = -14),
(iii)
dydx\dfrac{\mathrm{d}y}{\mathrm{d}x}.
[1]
(iv)
the integer value of xx for which the gradient of the curve is 22 and the corresponding value of yy.
[3]
(v)
Find the equation of the tangent to the curve at PP.
[1]