Question Detail
Question
Value of \( k \) for the function \( y = (4x\sqrt{x} + k)/7x \) if tangent at \( x=1/4 \) is parallel to \( 44x + 7y - 5 = 0 \)?
Correct Answer
Option A is the correct answer.
Detailed Explanation
Slope of line is -44/7. Derivative simplified: ( y = 4/7x^{1/2} + k/7x^{-1} \implies y' = 2/7x^{-1/2} - k/7x^{-2} ). At 1/4, ( y' = 4/7 - 16k/7 = -44/7 \implies 4 - 16k = -44 \implies 16k = 48 \implies k = 3 ).
Hint
Equate the slope of the curve to the slope of the parallel line.