Based on the following given information answer the question
Consider the function \(f(x) = x|x|\), \(x \in \mathrm{R}\).
The slope of the tangent drawn at the point whose x coordinate is 2 on the curve \(y = x|x|\).
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4
Near x = 2, x is positive, so |x| = x and
\(y = x^{2}\)
\( \displaystyle \frac{dy}{dx} = 2x \)
The slope of the tangent at x = 2:
\(2 \times 2 = 4\)