The curve $D$ has equation $y = -\ln(2x^2 - x + 1)$. $D$ crosses the positive $x$-axis at \(

Question

The curve $D$ has equation $y = -\ln(2x^2 - x + 1)$. $D$ crosses the positive $x$-axis at $A$. Use a non-calculator method to find the equation of the tangent to $D$ at $A$ in the form $ax + by = c$, where $a$, $b$ and $c$ are integers to be found.[4] Sketch the graphs of $D$ and the tangent found in part (a) on a single diagram, stating the exact coordinates of the points of intersection with the axes.[2] $R$ is the finite region bounded by the curve $D$, the tangent in part (b) and the $y$-axis. Find the area of $R$, giving your answer correct to $2$ decimal places.[2]

Accepted Answer

(a)$y=-x+\frac{1}{2}$ (c)0.08

2024 NYJC H1 Q4

2024 NYJC H1 Q4