The Mathematical Methods for Physicists

1. a.
b. f(1) + f(2) + f(5.5) = 40 + 40 + 82.5
= 162.5
c. f(a) = 95
This value can be offered only by the function :
f(a) = 25a – 55
So,
95 = 25a – 55
a = 6

2. a. g(x) = -x2 + 4x + 1
= -(x2 – 4x – 1)
= -(x2 – 4x + 4 – 5)
= -(x – 2)2 + 5
For calculating turning point, we differentiate it-
g’(x) = -2x + 4
0 = -2x + 4
x = 2

b.
c. For calculation x-axis intersection, put g(x) = 0 in the function-
0 =-x2 + 4x + 1
x=−b ± √ b2−4 ac
2 a
After calculations-
x = -0.236 and x = 4.236
Points are : (-0.236, 0) and (4.236, 0)