Science:Math Exam Resources/Courses/MATH102/December 2013/Question A 05/Statement

Consider the function $y=\cos (x)$ and the tangent line to this function at the point $x=\pi /2$. Using that tangent line as a linear approximation of the function would lead to

(a) overestimating the value of the actual function for any nearby $x$.

(b) underestimating the value of the actual function for any nearby $x$.

(c) overestimating the function when $x>\pi /2$ and underestimating the function when $x<\pi /2$.

(d) overestimating the function when $x<\pi /2$ and underestimating the function when $x>\pi /2$.

(e) overestimating the function when $x<0$ and underestimating the function when $x>0$.