The curve $C$ has equation $y = \frac{3}{2}x^3 + \frac{1}{2} + \mathrm{e}^{1-x^2}$. Find \(\frac

Question

The curve $C$ has equation $y = \frac{3}{2}x^3 + \frac{1}{2} + \mathrm{e}^{1-x^2}$. Find $\frac{\mathrm{d}y}{\mathrm{d}x}$. Hence, find the equation of the tangent to $C$ at the point $P$ where $x = 1$. Give your answer in the form $y = mx + c$, where $m$ and $c$ are exact real values.[5] The tangent to $C$ at $P$ intersects the $x$-axis at $A$ and the $y$-axis at $B$. Find the length of $AB$.[4]

Accepted Answer

(i)$\frac{\mathrm{d}y}{\mathrm{d}x} =\frac{9}{2}x^2-2xe^{1-x^2}$, $y=\frac{5}{2}x+\frac{1}{2}$ (ii)Length of AB= 0.539

2024 TMJC H1 Q4

2024 TMJC H1 Q4