Question

Question 2: Find for the following functions: (1) y=-42x2-3x -! 7x? -5x + 9 (3) y= x+5 (5) Y= 7+3 (y = (3x* + 3x + 2)(x+1) (7) y =(5x + 7x) Page 1 of 2 Question 3: (0) Find the slope of the graph of y=f(x) = 3x - 6x +1 at the point (2,1) (ii) Find the equation of the tangent line to the curve y = f(x) = x*-10x2 + 9 at x=-1 (iii) Find the equation of the tangent line to the curve y = x +13 at x = 7 Question 4: (A) For the coast function C(x)=0.02x' +0.06x +30x+140, find the marginal cost at x=800 (B) Find the marginal revenue if R= 15 (©) Find the marginal cost if C = 300-Vq2 + 20 (D) If the demand equation for a manufacturer's product is p -4q+12-9, where p is in dollars, (i) Find the marginal - revenue function. (ii) What is marginal revenue when q - 15 units?

Answer 1

Answer question (2): (1) given y = - 42 x zx' o u t dy = d (-4an 3x) = -42X-7 X - _ 3x D x l-1] = 29488 3 x 2 ) = mx!! -7-1 X - X-7 (2) given y = 5 x + 11 12 (58x2x) + (15 x -4.541) X-4 .) to (3) (3) given y = 750_5449 given y = x3 +5 vr die (199) Py). v. -up' (x*5) (787_5x+9) (182_58+9) + (x+5) (3 4 5 (21375) (x23-5+)– 18_5x+9)(3x4+0) sed (845) 14x3+70x-523-25-2134 +15239 (3+5) -2124 +24x² - 270 +70K-25 3151

(t) given y = 1/5 + 1 (84% /3 = x 220564644) X (5.) goen, y XV+3 G3 * 4.(922) – 4123/"(243)/5 [(x+3/s ] (20+3622 55+ "[axaexo) -(62 2. Kufanya px+)] (xV+3) / (+375 (972 25 4 3 2 1 _ (9 122) * 6+2 + 2x 11

278164338, - dx (423) DEO (1943) BOX64.35 (sust - 23 (9232)+(9222) 5 6232)$. 60+2)7. (043) Lidy. 2784(04+3) – 2x GX32) - 2774+81x1 – 1884+ 4x 5 (9232) 4 (N + 3) / 9x4+81X+ 5 (923-2) + 3 i dy - (6) given, y = 6x² + 3x+2)(x + 1) =) y = 3xº+3x5+2x+ 3x4 +3x+2 dy - d (3x91376+825+ 3x4+3x+2) I = (3x 9 x 9 + 6 x 6 x 3 + (2x5xa5-4 (Bx4 24-1) +3+0 dy - 9788+18x5 +10x4 +12 3+3 given y = (583 + 72) 9 (7) de [1613470)") = 9(52%)x)" (5x2xV+7).

..dy = 9 (5x3+4x)®(15x+1) .de Question no:3. 6 given y = f(x)= 3x² - 6x +1 , at point (21) claim: we have to find the slope of fre) at (2,1) *NOTE: The elope of f(x) at xea is equivalent to the slope of its tangent line at k=a q Za tangent line to fix) et x-a is The slope of tangent line to f(x) at n=a lim flath)-fia) provided this limit ho -enists. at Consider, tim f(a+h)-f(2) hto h - 13(a+h)-6 (2+2)+1- [3x2 - 6(2)+17 = lim 3 (4tht4h)-12-6h+1 -12 +12-1 ho - = lt 12+ 3 hr + 1gh-6h-12 ho - =lt 3hr+6h hoh

= lt k( 3h+6) ho & it (3h+6) ho = 3(0)76 the slope of f(x) = 6 Alternative method: n given in fred= 3x7_6XH fox) = f'(x) = 68-6 = f'()=6(2)-6 = 6 e. The slope of the graph of y=f(n)=3* - 6x +1 at (2,1) i 6 (1) given the equation of the curve y=x4-10x19 at X=-1 * The slope of the curve of f(x) at u=a is f(a) y = f(x)= 4x3_20x f(-1) = 4(-1)3_20(-1) = - 4+20= 16 = plope The equation of the tangent line to the cuire y flas at (x,y) is y-Y,= m (x-1) Since y = f(x) = x4_1027+9 , at X=-1, fl-1)= (17_10(-1)+9 = 1-10+9=0 . (4,4) = (1,0) zm

The equation of the tangent line to the cusve 4 -- 0 - 1 (1-(-)) y = 16x+16 given the cusve y-from- JAVH13 at x= 7 ~ y'= f'(x) = f (+13) Z (2x+0) = {( x H2) = (2x) = f(x- 42% = f'() = 7 {N+13)% = 0.889 = slope = 0.889 = slope Em at X-7, y = f(7) = 549+3 = 152 = 1.844 .:(,), ) = ( 7.874) The equation of the tangent line to the cure fin is y-y = m(x-X1) Y-7.814 = 0.889) (x-7) y- 7.874= 0.889) - 6.223 y = 0.889)x-1-651