Applications Of Derivatives Question 74
Question: If at each point of the curve $ y=x^{3}-ax^{2}+x+1, $ the tangent is inclined at an acute angle with the positive direction of the x-axis, then
Options:
A) $ a>0 $
B) $ a\le \sqrt{3} $
C) $ -\sqrt{3}\le a\le \sqrt{3} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ \frac{dy}{dx}=3x^{2}-2ax+1 $
Given that $ \frac{dy}{dx}\ge 0 $ or $ 3x^{2}-2ax+1\ge 0 $
for all $ x $ or $ D\le 0 $ or $ 4a^{2}-12\le 0 $ or $ -\sqrt{3}\le a\le \sqrt{3} $
BETA
