Differentiate $\ln(5ax + 4x^2)$ with respect to $x$, where $a$ is a constant. The diagram

Question

Differentiate $\ln(5ax + 4x^2)$ with respect to $x$, where $a$ is a constant. The diagram shows the curve $C$ with equation $y = 2\mathrm{e}^{2x} + 1$. Without using a calculator, find the equation of the tangent to $C$ at the point where $x = 0$, giving your answer in the form of $y = mx + c$, where $m$ and $c$ are constants. Find the exact area of the region bounded by $C$, the tangent found in part (b)(i) and the vertical line that cuts $C$ at the point where $y = 2\mathrm{e}^2 + 1$.

Accepted Answer

(a) $\frac{5a+8x}{5ax+4x^2}$, where $5ax+4x^2>0$. (b)(i) $y=4x+3$. (ii) $e^2-5$ square units.

2024 EJC H1 Q4

2024 EJC H1 Q4

Solution:

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