The curve with the equation given below is called a kampyle of Eudoxus. Find the equation of the tangent line to this curve at the point (-1, 2). y2 = 5x4 − x2

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

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.