What is the equation of the tangent line of #f(x)=cos^3x^2 # at #x=0#?

Question

4320 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-02T16:59:37

Hence equation of tangent is y=1

Let
#y=cos^3x^2#

Slope of the tangent is

#dy/dx=3cos^2x^2(-sinx^2)(2x)#

#m=-6xcos^2x^2sinx^2#

at x=0

#m=-6xx0xxcos^2 0^2sin0^2#

#m=0#

point of tangency is

#y=cos^3x^2=cos^3 0^2=cos^3 0=(cos0)^2=1^2=1#

Hence equation of tangent is y=1