A curve is described by 𝑦=𝑝𝑥2+𝑞𝑥, where 𝑝 and 𝑞 are constants.
a. Find an expression for the gradient of this curve at any point.
b. Given that at the point (1,−2) the gradient is 6, calculate the values of 𝑝 and 𝑞.
c. Show that the equation of the normal to the curve at the point (1,−2) can be written as 𝑥+6𝑦+11=0.
a.
"y=px^2+qx""grad (y)=(px^2+qx)'=2px+q"
b.
"q=-2-p""2p-2-p=6"
"p=8, q=-10"
c.
Find the slope of the normal at the point "(1, -2)"
The equation of the normal at the point "(1,-2)" is
"6y+12=-x+1"
Then he equation of the normal to the curve at the point "(1,\u22122)" can be written as
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