Let f be a differentiable function on R such that f (2 )=1 ,f^ ' (2 )=4. Let limx 0 (f (2+x ) )^3/x=e^ . Then the number of times the curve y=4x^3-4x^2-4 ( -7 )x- meets x axis is:

Question

Accepted Answer

Correct answer: C. (c) limx 0 (f (2+x ) )^3/x= (1^ form ) e^ lim_x 0x^3 (f (2+x )-1 )=e^ lim_x 3f^ ' (2+x ) =e^3f^ ' (2 ) =e^12 ⇒ =12 y=4x^3-4x^2-4 (12-7 )x-12 y=4x^3-4x^2-20x-12 y=4(x^3-x^2-5x-3) =4 (x+1 )^2 (x-3 ) It meets the x-axis at two points

$Let f be a differentiable function on R such that f (2) = 1, f^{’} (2) = 4 . Let lim x \to 0 (f (2 + x))^{3/ x} = e^{α} . Then the number of times the curve y = 4 x^{3} - 4 x^{2} - 4 (α - 7) x - α meets x axis is:$

Solution

More Limits PYQs