What is the equation of the line tangent to f(x)=cos x + sin^2 x at x=0?

1 Answer
Jan 5, 2016

y = 1

Explanation:

f(x) = cos x + sin^2x

f'(x) = - sinx + 2sinx ( cosx) = 2sinxcosx - sinx

at x = 0:

f'(0) = 2sin0 cos0 - sin0 = 0

now since the slope of the tangent line = 0 the tangent will be parallel to the x-axis with the equation y = k where k is a constant.

f(0) = cos 0 +(sin0)^2 = 1

rArr y=1 is the equation of the line tangent.