12. Fcchncr's law describes the relationship between \"stimulus intensity" 1', such as the brightness of a light in lumens, and \"perceived intensity" p(.r)_. such as the perceived brightness of a light by a viewer. It is given by pm = k104i) , m where k and m are positive constants. The domain is restricted to :r 2 m. (a) [3 marks] Find p'(r), and state all intervals in the domain where p(:.:') is increasing. (b) [3 marks] Find p"(x), and state all intervals in the domain where p(x) is concave up. (Answers should be written in the box. Justification should be outside the box.)(c) [3 marks] Draw a large sketch of the graph of p(x) on the axes below, clearly labelling any intercepts, asymptotes, extrema and inflection points. (d) [3 marks] At a given stimulus intensity , the discrimination threshold is the mini- mum increase in stimulus intensity such that the corresponding increase in perceived intensity is equal to or greater than a constant Ap. According to this model, are discrimination thresholds at high stimulus intensities greater than discrimination thresholds at low stimulus intensities? Give your answer and justify it in a few sentences.(e) [2 marks] Stevens' power law is sometimes taken by psychophysicists (who stud}r stimuli and perceptions) to supersede Fechuer's law. It proposes that perceived intensity x) is related to stimulus intensity 1' according to 6 6(1) = In: ._ Where a is a parameter that depends on the type of stimulus. and k is the same positive constant as in Fechner's law. If p(.r) and ts) are meant to describe the same relationship, in which of the following inten'als is the parameter (I? Remember to justify your answer. A. (00, 1) B. (1,0) C. (0,1) D. (1,00)