Question

find the values of x at which the curve y = f(x) has a horizontal tangent line.
f(x)= (2x + 7)^6 * (x-2)^5

Answer 1

\[y=(2x+7)^{6}*(x-2)^{5}\]
\[y'=5(2x+7)^6*(x-2)^4(1)+6*2(x-2)^5(2x+7)^5\]
\[0=5(2x+7)+12(x-2)\]
\[0=10x+35+12x-24\]
\[22x=-11\]
\[x=-1/2\]