Question

If the equation of the normal to the curve y = 2x2 + 4.5x + 1 is y = −2x + c, find the:

a) coordinates at the point of tangency

b) value of c.

Answer 1

take the derivative to get a formula for the slope of the tangent line
the normal line has slope as the negative reciprocal of the tangent , so the slope of the tangent line will be \(\frac{1}{2}\)
set the derivative equal to \(\frac{1}{2}\)
solve for \(x\)

Answer 2

I've done that now and I tried to continue on from there but the answer I got is different from the book's answer.

Answer 3

y = 2x2 + 4.5x + 1
y' = 4x + 4.5

since y' = slope of tangent; -1/y' = slope of normal

-1/y' = \(\Large -\frac{1}{4x + 4.5}\)

Answer 4

for what value of x does y' = -2?

Answer 5

gotta readjust my glasses ..

the normal to the curve has the equation: -2x+c

Answer 6

satellites workings are becoming more clear to me now :)

Answer 7

for what value of x does y' = 4x + 4.5 = 1/2

Answer 8

4x + 4.5 = 1/2

8x + 9 = 1

8x = -8

Answer 9

yes, I also got x = -1 for that step.

Answer 10

ok, then when x=-1, what does y = for the point we are looking at?

y = 2x2 + 4.5x + 1

y = 2 - 4.5 + 1

Answer 11

oh wait my bad, I missed the plus one at the end because I forgot to write it in the beginning first equation ==, let me try again.

Answer 12

ok, I got it, thanks so much.

Answer 13

Ny = -2x +2(-1) + y
|---------|
= c

youre welcome