Let f(x)=(x^4+x^3+x^2+x+1)(x^5+x^3+x+2) find the equation of the line tangent to the curve when x=-1?

1 Answer
Jim G.
Feb 24, 2018

#y=11x+10#

Explanation:

#•color(white)(x)m_(color(red)"tangent")=f'(-1)#

#"differentiate using the "color(blue)"product rule"#

#"given "f(x)=g(x)h(x)" then"#

#f'(x)=g(x)h'(x)+h(x)g'(x)larrcolor(blue)"product rule"#

#g(x)=x^4+x^3+x^2+x+1#

#rArrg'(x)=4x^3+3x^2+2x+1#

#h(x)=x^5+x^3+x+2#

#rArrh'(x)=5x^4+3x^2+1#

#rArrf'(x)=(x^4+x^3+x^2+x+1)(5x^4+3x^2+1)#

#color(white)(rArrf'(x)=)+(x^5+x^3+x+2)(4x^3+3x^2+2x+1)#

#rArrf'(-1)=(1)(9)+(-1)(-2)=11#

#f(-1)=(1)(-1)=-1rArr(-1,-1)#

#rArry+1=11(x+1)#

#rArry=11x+10larrcolor(red)"equation of tangent"#

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