Additional Mathematics 0606 / Calculus — Differentiation 1 / 3.443.44: Gradient condition and finding f(x)0606/13/O/N/21 — Question 10 · 9 marksMark as done · Save for later · Show all solutionsA curve y=f(x)y = f(x)y=f(x) is such that dydx=(2x3+5)12+x−2\dfrac{\mathrm{d}y}{\mathrm{d}x} = (2x^{3} + 5)^{\frac{1}{2}} + x^{-2}dxdy=(2x3+5)21+x−2 for x>0x > 0x>0. The curve has gradient 101010 at the point (3, 192)\left(3,\ \dfrac{19}{2}\right)(3, 219).(a)Show that when x=11x = 11x=11, dydx=52\dfrac{\mathrm{d}y}{\mathrm{d}x} = 52dxdy=52.[5]▸ Answer(b)Find f(x)f(x)f(x).[4]▸ Answer▸ Official mark scheme← 3.6: Differentiation, small increments and connected rates3.45: Derivative of a composite power and stationary point →
