Question

a) Find the linear approximation of the function f(x)=4cos(3x^2) near x = 0

b) Use the approximation found in part (a) to estimate the value of f(pi/20)

Answer 1

f'(x) = -24x sin(3x^2)
f'(0) = 0

So, you want the line with slope=0 through (0,4). Duh. y=4

Kind of a dumb place to approximate, eh? With a horizontal tangent, and all that.