For , the value of is even though and are both non-zero at . Which statement best…
MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
For y=xsinx, the value of y′(0) is 0 even though dxd(x) and dxd(sinx) are both non-zero at x=0. Which statement best explains this?
(a) Because both sin0 and cos0 are zero, the two terms in the product rule each evaluate to 0.},{
(b) Since y(0)=0, any tangent drawn at the origin must be horizontal, so the derivative is 0.},{
(c) In the expression for y′, one term contains the factor x, which becomes 0 at x=0, making the whole sum 0.},{
(d) Using the small-angle approximation sinx≈x, the function becomes x2 near x=0 whose derivative at 0 is 0.}]},