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A curve C1 = ax4 + bx3 + cx2 + dx + e intersects y-axis at -7. The slope of C1 at this point is 6. Also, the curve intersects another curve 2x - 7 at x = 1. The value of (a + b + c + d + e) is
  • a)
    is 1 for all values of x
  • b)
    can be determined only at three values of x and is 1
  • c)
    can be determined only at two values of x and is -5
  • d)
    can be determined only at one value of x and is -5
  • e)
    cannot be determined for any x
Correct answer is option 'D'. Can you explain this answer?
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A curve C1= ax4 + bx3 + cx2 + dx + e intersects y-axis at -7. The slop...
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A curve C1= ax4 + bx3 + cx2 + dx + e intersects y-axis at -7. The slop...
Given:

  • Curve C1= ax4 + bx3 + cx2 + dx + e

  • C1 intersects y-axis at -7

  • The slope of C1 at y-axis is 6

  • C1 intersects curve 2x - 7 at x = 1



To find: The value of (a b c d e)

Solution:
Intersects y-axis at -7

When x = 0, y = -7

So, e = -7


The slope of C1 at y-axis is 6

Slope of C1 at y-axis is equal to the derivative of C1 at x = 0

So, C1' = 4ax3 + 3bx2 + 2cx + d

When x = 0, C1' = d

Given that C1' at y-axis is 6

So, d = 6


C1 intersects curve 2x - 7 at x = 1

So, ax4 + bx3 + cx2 + dx + e = 2(1) - 7

=> a + b + c + d + e = -5


Value of (a b c d e)

From the above equations:

e = -7

d = 6

a + b + c + d + e = -5

Substituting e and d values in the third equation:

a + b + c = -4

As there are 4 variables and 3 equations, we can determine only at one value of x.

So, option D is the correct answer.
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A curve C1= ax4 + bx3 + cx2 + dx + e intersects y-axis at -7. The slope of C1at this point is 6. Also, the curve intersects another curve 2x - 7 at x = 1. The value of (a + b + c + d + e) isa)is 1 for all values of xb)can be determined only at three values of x and is 1c)can be determined only at two values of x and is -5d)can be determined only at one value of x and is -5e)cannot be determined for any xCorrect answer is option 'D'. Can you explain this answer?
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A curve C1= ax4 + bx3 + cx2 + dx + e intersects y-axis at -7. The slope of C1at this point is 6. Also, the curve intersects another curve 2x - 7 at x = 1. The value of (a + b + c + d + e) isa)is 1 for all values of xb)can be determined only at three values of x and is 1c)can be determined only at two values of x and is -5d)can be determined only at one value of x and is -5e)cannot be determined for any xCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A curve C1= ax4 + bx3 + cx2 + dx + e intersects y-axis at -7. The slope of C1at this point is 6. Also, the curve intersects another curve 2x - 7 at x = 1. The value of (a + b + c + d + e) isa)is 1 for all values of xb)can be determined only at three values of x and is 1c)can be determined only at two values of x and is -5d)can be determined only at one value of x and is -5e)cannot be determined for any xCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A curve C1= ax4 + bx3 + cx2 + dx + e intersects y-axis at -7. The slope of C1at this point is 6. Also, the curve intersects another curve 2x - 7 at x = 1. The value of (a + b + c + d + e) isa)is 1 for all values of xb)can be determined only at three values of x and is 1c)can be determined only at two values of x and is -5d)can be determined only at one value of x and is -5e)cannot be determined for any xCorrect answer is option 'D'. Can you explain this answer?.
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