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If x2 plus y4 equals 10x plus 7 then what is the slope of the tangent line at 1 -2 and what is the equation of that tangent line- and at what point are the lines tangent to the original equation?
Mbscharle
x^2+y^4=10x+7 @ (1,-2)
Rearrange to isolate y.
y=(-x^2+10x+7)^(1/4)
Take derivative.
y'=(1/4)*((-x^2+10x+7)^(-3/4))*(-2x+10)
y'=(-2x+10)/4*(-x^2+10x+7)^(3/4)
Sub in x=1.
y'=8/2*(16)^(3/4)
y'=2/8
y'=1/4
y'=m=slope=1/4
Sub m and (1,-2) into linear equation (tangent line).
m*(x-x1)=y-y2
(1/4)(x-1)=y+2
Isolate y.
Equation of tangent line: y=(1/4)x-(9/4).
The third question is unclear.
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