Question

5. Suppose that the line tangent to the graph of y = f(x) at x = 3 passes through the points (-2,3) and (4, -1). What is the equation of the line tangent to f(x) at x = 3? (1) y=x+ (3) y = -x +5 (1) y= {x +3 (2) y 6. Let f(x) = 7 sin(x + 7) + cos2x. Compute f(13)(O). (1) 8 (2) 7 (3) -8 (1) -7 ----- 7. Differentiate f(x) - 1.6+3 Vã+1 (1) f'(x) [(3:4 –4x+3)/(2D) -(V++1)(4x3–4) (+1) (MI206) Page 1 of 1 (2) f'(x) 8(x-1) (3) f'(x) (4:23–4)-(1/2) (2+1)2 (4) f'(x) = (V++1)(1:3–4)-1(&_4x+3)/(2/7) (Vx+1) 8. Differentiate h(x) = (sin 3x) + 5.0 (1) W'(x) = 6(sin 3x)2 sin 3x +5 (3) '(x) = 3(sin 3.)2 +5 (2) W'(x) = 9(sin 3x) cos 3x + 5 (1) h'(x) = 3(sin 3x)2 cos 3. +5

Answer 1

solution: 5 equ of tangent line to fas at n-3 = equ of line which passes through two points (23) & (+). 364) Then, Eg" of line (tangent) to flera u 3-(-) -24 Y-(-) Y+ 2-4 -64-6= = 40-16 = 4n+16-6 = zby y = $(4x+10) y = -2 2 They option ② is correct. Note: er of line passing through ( ) & ( ) is y y GY (MO) X-24 -

written as eqr can be h'cks & using 2 da using in , weget ha 3 t² 3 (os3x + 5 hes = 9 +² 2083x + 5 weget using t= singh how - g (sin 3x)? Los 3x + 5 option ③ is correct answery لحي (15) Solutions Given fria tsinel - 4*20 t fm = sinn Jas= lsinki given [n] (graph of According to interval, foi = binu), lies below x-axis. So fas - sinn in [-to] We take

[Pg. 5) Now, find anti derivative F for flug = - sinu Su, J-sinn du O FR Cosn tc Ito Put no & For in , weget Fo Itc cao Thes, using in 1, weget F = -Hence option ② is correct.

(pg 3 x" - 4x +3 Differentiate with by using quotient rule f'c = [(5x + 1) (yn-y) - (nh Lun + 3). t (52 +1² This option 4 is correct. Note: If fun= gay ho hces p'os - gee). h'les Then In the given question, go= x -unt, how= 5+1 gimga yetu n'assare solutions Given, he - 0 (sin 3x)² + 51 find hase ? Differentiate worita n' & (&inza) + 5 dhe take sin 3x = t Dift witx 3 cs3x = d+ dre e eq" can be written as also in du at 3 Cos3x

199-2 Solution Given - 7 sin Titx) + cos2x Then, fo = -7 sinn & cosan sin (+) = -fin (I) quadrant How -7 lopu - 2 sinan goma sinn corn WTFm hung t let ( 2 Coin funa 7 Logn + 8 sinan g'ona-sinn -7 sinn +16 osan Note : -7 cosx - 32 Sinza fcm dem 7 sinn - 64 Cosen 7 win + 128 sinau -7 sina + 256 (osar Vui S - 7 cose - 512 sinan ix 7 sinn - 1024 coser withis shot tuson L xar WTFm 95 oh -7 sunt XIN 8192 -7 con- uzhig TS ملا get Put no X111 8 -7-0 L-= is correct answer. They option f