Question

Graph of f Let f be the continuous function defined on (-1,8) whose graph, consisting of two line segments, is shown above. Let g and h be the functions defined by g(x) = h (2) = 5e-9 sin 2. -x +3 and (a) The function k is defined by k (x) = f(x) g(). Find k' (0) (b) The function m is defined by m (x) = 2007). Find m' (5). c) Find the value of x for -1 < x < 2 such that f' (2)=h' (2).

Answer 1

77 B (2,7) (8,3) (-1,1% gsinx. g(x) = J x²_0+3 and h(x) = 50% equation of line BC (8,3), (2,7) Y-3 = 7 -3 (0-8). 2 -8 4-3 = -2(x-8) 9-3 = -2*+ Y+x +3 (y + 2 x = 25 equation. OB. (2,744-1, 1 9-7 = 1 7 (x-2) -1-21 9-7- 6 (1-2) y 7 = 2x - 4 ly-2x = 3 2)

f(x) = 2x+3 X2 2 < @ 9(x)= x²_x+3 and h(x)= 5e²gsina. k = f(x).918) K'(X) = f()-9'(x) + g(x). F'(X) k (o)- flogg!(o) + g(0) f'(o) = [2(0)+3] 1.(2x-1) + 3.(2) 25x2_x + 3 - 3(0-1) +33 (2) 2.3 T5 = -3+4x3 253 6 m= f(x) m'15) = ? 2918) 2 L (962)32 mit 1 (0) Aft Ca.ban (0) 4034C) 25) = 1 [17:231-23- GS. 265)-1 2923 (-36 - (E-)). 23

find the value of x for – I LIL2 st f'()) = '(&) f(&) = 2x+3 -ILAL2. h(x) = Seda_g sina. 2 = sea - I Cosa. 2-50% -- 9 Casx 50?_2= glasa X3 Only spoint of intersection of sex_2 2 9 Cast. i.e point A.