Applications Of Derivatives Question 413
Question: If the curve $ y=ax^{2}-6x+b $ passes through (0, 2) and has its tangent parallel to the x-axis at $ x=\frac{3}{2}, $ then
Options:
A) a = b = 0
B) a = b = 1
C) a = b = 2
D) a = b = -1
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ y=ax^{2}-6x+b $ passes through (0, 2). i.e., $ 2=0-0+b $ or $ b=2 $
Again, $ \frac{dy}{dx}=2ax-6 $ At $ x=\frac{3}{2},\frac{dy}{dx}=3a-6 $ Since tangent is parallel to x-axis, $ \frac{dy}{dx}=0 $ or $ 3a-6=0 $ or $ a=2 $ .
Hence, $ a=2,b=2 $ .
BETA
