SocialTwist Tell-a-Friend

Ask a Question? Get an Answer!


Question: Which of the following will be the cost function for the marginal cost function C′(x) = 2x + 3x2 when cost of 2 units is $12?


A ) C(x) = - x2 + x3
B ) C(x) = x2 - x3
C ) C(x) = x2 + x3
D ) C(x) = x2 + x3 + x

Steps to derive

1 C′(x) = 2x + 3x2
 [Given.]

2 Since, cost of 2 units is $12, we have C(2) = 12.
 [Given.]

3 C(x) = ∫(2x + 3x2)dx
 [Integrate both sides.]

4 C(x) = x2 + x3 + k

5 12 = 22 + 23 + C
 [Substitute x = 2, C(2) = 12.]

6 12 = 4 + 8 + C

7 C = 0

8 Thus, the cost function is C(x) = x2 + x3.



Hence the right answer is Option C

Click Here To Go Back


Few Other Questions -

  • If f(v)= 3v + 5if v ≤ 0,= 4v2 + 9v + 8if v > 0,then evaluate limv→0 f(v)...
  • Two figures are similar if ______..
  • The area of trapezoid ABCD is 9 cm2 and trapezoid PQRS is 16 cm2. If the two trapezoids ar..
  • If f(p) = 2[p] + 3, g(p) = 32[p] - 5 where [p] represents the greatest integer ≤ p, the..
  • Two regular pentagons ABCDE and PQRST are similar. The length of a side of ABCDE is 5 cm...
  • If [q] denotes the greatest integer ≤ q for all q ∈ R, then evaluate limq→5(..
  • Trapezoid ABCD is similar to trapezoid MNOP. Find the ratio of their areas. [Given a = 8 u..
  • Evaluate limr→9π2+ (3[sin r] + 48) where [r] represents the greatest integer ≤ ..
  • The figure shows two regular pentagons which are similar. If the area of the larger penta..
  • Iff (z) = 4sin [z]10[z]if [z] ≠ 0= 0if [z] = 0where [z] is the greatest integ..
  • Evaluate: lims→0 [e11s-17s]..
  • The area of the smaller regular hexagon is 120 cm2. Find the area of the shaded portion of..
  • If g(v) = 41[v] sin (6v), where [v] denotes the greatest integer function, then choose the..
  • Evaluate: limr→0(e28r-e8rr)..
  • Evaluate: lims→0 [27s-15s]..
  • If [v] denotes the greatest integer ≤ v for all v ∈ R, then evaluate limv→5+[..
  • Evaluate: limk→0 [e7k-1e5k-1]..
  • Evaluate: limn→0 [23n-155n-1]..
  • Evaluate: limv→ 0(e4v-1v+81-9)..
  • Evaluate: limz→0 [135z-87zz]..
  • Evaluate: limw→0 (e7w-e3we6w-e3w)..
  • Evaluate: limn→0(72tan 3n-1n)..
  • A race track is in the form of a ring. The ratio of inner radius to the outer radius is 3 ..
  • Evaluate: liml→0 (5l-10l+15l-20ll)..
  • The circle R is similar to the circle S. The ratio of their radii is 2 : 3. If the area of..
  • Evaluate: limk→0 [2k+3k+4k+ . . . . +33k-32k]..
  • Evaluate: limu→0(3ln(1+5u)8u)..
  • Evaluate: limu→0 [70u-7u-10u+1u2]..
  • Evaluate: lims→0(8s-8-s38s)..
  • Evaluate: limy→0 [10ye6sin 4y-1]..
  • Evaluate: limp→0 (3 ln(1+8p)7 ln(1+10p))..
  • Evaluate: limv→2 (ev-e24v-8)..
  • Evaluate: limq→1 (10 ln q7(q-1))..
  • Evaluate: limw→0 (9 ln(1+8w9)13 ln(1+11w9))..
  • Evaluate: liml→0 [2ln (1+48sin 8l)4l]..
  • Evaluate: limr→0(8ln(cos r)10(cosr-1))..
  • Evaluate: limy→0 [5 ln (1+4sin 9y)22 ln (1+9sin 9y)]..
  • Evaluate: liml→0 (9ln(1+4sin2 4l)10ln(1+5sin2 4l))..
  • Evaluate: limk→0(5ln(1+5k)ln(1+10k)10k2)..
  • Franklin paid a carpenter $4 to polish his wooden table which is 12 ft long. His neighbo..
  • Evaluate: limk→0(e7k-e-7k11ln(1+k))..
  • Which of the following figures has a line of symmetry?..
  • Evaluate: limk→∞ [5+8cos 5k12k+5]..
  • Evaluate: limm→0 (49m cos (73m))..
  • Evaluate: limy→∞ (7sin 4y + 19y5y)..
  • Evaluate: limx→∞ (5cos20 4x+24+9x)..
  • Evaluate: limq→0 (8q2 sin (52q) + 29 )..
  • For all y ∈ [- 1, 1], y8+7 ≤ f (y) ≤4y8+7. Find limy→0..
  • Evaluate: limk→∞ [2sin4 4k+6k+372k+5]..
  • Evaluate: limp→0 (8p(sin5p + cos5p)+13)..
  • Evaluate: limv→0(4v3(6sin5v2 - 8 cos5v2)+33)..
  • Evaluate: lims→0 (5s2 sin2s cos2s + 14)..
  • Evaluate: limp→∞(12sin (18p) + 16cos (18p)20p2)..
  • If 9cos z + 40 ≤ h(z) ≤ 49 + z4 for all z ∈ [- 1,1], then find limz→0 1h(z..
  • Evaluate: limk→∞ [6cos 12k10k6]..
  • Evaluate: limm→∞ [6sin (12m)10m8]..
  • Evaluate: limn→∞ (9sin 11n19n10)..
  • Evaluate: limq→∞ 9q4-sin 9q+1111q4+9..
  • If 9sin (p18)+2712 ≤ g(p) ≤ 9sin (p6)+2712 for all p ∈ [- 1, 1] and ..
  • If 5cos (n4)+107 ≤ h(n) ≤ 5cos (n12)+107 for all n ∈ [- 1, 1], then e..
  • If 2sin 11l + 7 ≤ g(l) ≤ 9 , then find liml→π2 g(l) by assuming that it..
  • 9l4+1813 ≤ f (l) ≤ 9l2+1813 , where l ∈[- 1, 1] and liml→0 f (l)..
  • If 9sin12l+ 408 ≤ f (l) ≤9sin6l + 408 for all l &..
  • If the areas of two similar decagons are 81 ft2 and 225 ft2, then find the ratio of their ..
  • This lists the number of points Cassie'steam scored in each of their games. 17  22 &n..
  • Evaluate: limx→∞ 3cos (16x)6x2..
  • A light a m above the ground causes a boy b m tall to cast a shadow s meters long measured..
  • If 25+81k4 ≤ f (k) ≤25+81k2 for all k ∈ [- 1, 1], then eval..
  • The figure shows a pair of similar hexagons. Find the value of x. [Given AG = 18, GB = 1..
  • If 3cos28q+182 ≤ g(q) ≤3cos14q + 182 for all q ∈ [- 1,..
  • Smith wants to make an advertisement board similar to another advertisement board having a..
  • Anna has a flower garden of 15 m × 20 m, which has 50 bushels of flowers. She decide..
  • A class room and the school library are in the shape of squares. The area of the class roo..
  • Trapezoid ABCD is similar to trapezoid EBFG. Find AD‾ and DC‾. [Given a = ..
  • Elizebeth is a ft tall and casts a shadow of x ft. She stands next to a tree and observes ..
  • Two similar polygons have corresponding sides with lengths in the ratio of 2 : 3. The sum ..
  • D, E, F are the midpoints of the sides BC‾, CA‾ and AB‾ respectiv..
  • In the trapezium PQRS, PQ‾ || RS‾ and PQ = 2RS. If area of ΔPOQ = 10..
  • In the given figure ABCD, AB‾ is parallel to DC‾. Area of ΔOAD = 8 s..
  • The basket ball court of a school is 64 ft long and 50 ft wide. The school authorities pai..
  • Tom plans to make some repairs on the roof of a building. He needs a ladder to reach the r..
  • Find AB‾, if the two polygons are similar. [Given AD = 7, SP = 5, AB = 2x + 3 ..
  • The church is on a hill top as shown in the figure. The figure is drawn to a scale of 1 : ..
  • Identify the incorrect statement.I. A rotation is a transformation that turns a figure abo..
  • Find the angle of rotation...
  • If g(y) = 2y + 8, limy→2 g(y) = g(2) and h(y) = 3y2, then evaluate limy→2 h(g(..
  • If g (n) = (1 - n + n2 - n3 + . . . . . . . + n330), then evaluate limn→1 g (n)...
  • If h(z) = 1 + 3z + 5z2 + 7z3 + . . . . . + 189z94, then find limz→1 h(z) ...
  • Rotate the given figure, 210° about the point P...
  • Recognise the figure which has rotational symmetry with an angle of rotation as 120°...
  • Identify the center of rotation of the following figure...
  • If h(y) = 4y2, limy→3 h(y) = h(3) and g(y) = 3y + 11, then find limy→3 g(h(y))...
  • Mark and Dennis are playing ferris wheel which is rotating counter clockwise. If they are ..
  • Select the rotational image of the given figure after a rotation of 300° in counter cl..
  • Which of the following figures is not the rotational image?..
  • Identify the figure which has rotational symmetry...
  • What is the angle of rotation about the point P that maps figure 1 to figure 2?..
  • What are the coordinates of the point P (3, 4) when rotated by 180° in the counter clo..
  • The clock shows 3'o clock. Through what angle should the hour's hand be rotated to show 12..
  • Find the angle of rotation...
    		•