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

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Answer 1 · 2016-09-19T06:16:02

Equation of tangent is #y=2#.

At #x=0#, #f(x)# takes the value #f(0)(=cos0+cos^2 0=1+1^2=2#

Hence, we are seeking a tangent at point #(0,2)# on the curve.

The slope of tangent at #x=0# is given by #f'(0)#

As #f(x)=cosx+cos^2x#,

#f'(x)=-sinx+2cosx xx (-sinx)# and

#f'(0)=-sin0-2cos0xxsin0=0-2xx1xx0=0#

Hence slope of tangent is #0# and it passes through #(0,2)#

Hence, equation of tangent is #y-2=0xx(x-0)# or #y=2#
graph{(y-cosx-(cosx)^2)(y-2)=0 [-5.155, 4.845, -1.24, 3.76]}