Question
Question: The curve y = ax<sup>3</sup> + bx<sup>2</sup> + cx is inclined by 45ŗ to x-axis at origin and it tou...
The curve y = ax3 + bx2 + cx is inclined by 45ŗ to x-axis at origin and it touches x-axis at (1,0). Then-
A
a = –2, b = 1, c = 1
B
a = 1, b = 1, c = –2
C
a = 1, b = –2, c = 1
D
a = –1, b = 2, c = 1
Answer
a = 1, b = –2, c = 1
Explanation
Solution
y' = 3ax2 + 2bx + c
at (0, 0), y' = 1, c = 1
at (1, 0), y' = 0, 3a + 2b + 1 = 0
⇒ on solving a = 1, b = –2