The function $$\(\mathrm{f}\)$$ is defined by $$\(\mathrm{f}(x)=\frac{1}{3 x+2}+x^{2}\)$$ for $$\(x<-1\)$$. Determine whether $$\(\mathrm{f}\)$$ is an increasing function, a decreasing function or neither. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_m20_qp_12 Year：2020 Question No：1
Answer:
\[
f^{\prime}(x)=\left[-(3 x+2)^{-2}\right] \times[3]+[2 x]
\]
\(<0\) hence decreasing
f^{\prime}(x)=\left[-(3 x+2)^{-2}\right] \times[3]+[2 x]
\]
\(<0\) hence decreasing
Knowledge points:
1.7.2 use the derivative of (for any rational ), together with constant multiples, sums and differences of functions, and of composite functions using the chain rule
1.7.3 apply differentiation to gradients, tangents and normals, increasing and decreasing functions and rates of change (Including connected rates of change, e.g. given the rate of increase of the radius of a circle, find the rate of increase of the area for a specific value of one of the variables.)
Solution:
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