aubreyfoster
28.08.2020 •
Mathematics
Indicate in standard form the equation of the line through the given points. P(0, -4), Q(5, 1) Enter your answer into the blank equation box. a0
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Ответ:
y= (-9/2)*x-5/2 or 2y+9x+5=0
Step-by-step explanation:
given the following equation
y² = 5*x⁴ - x²
we can take the derivative with respect to x in both sides to get the slope of the tangent line , and knowing that y=f(x) we can apply the chain rule , therefore
d(y²)/dx = d(5*x⁴ - x²)/dx
2*y*dy/dx = 5*4*x³ - 2*x
dy/dx = (10*x³-x)/y
replacing values (x=-1,y=2)
m=dy/dx = (10*(-1)³-(-1))/2 = -9/2
now from the equation of the line
y= m*x+h
we know that (x=-1,y=2) belongs also to the line since it is tangent to the curve, thus
2= (-9/2)*(-1) + h
h = 2 - 9/2 = (-5/2)
thus
y= (-9/2)*x-5/2
or
2y+9x+5=0