Question

Find the equations of the tangent and normal to the given curves at the indicated points:

Answer 1

\[y = x^4 - 6x^3 + 13x^2 - 10x + 5\] at (0,5)
\[y = x^4 - 6x^3 + 13x^2 - 10x + 5\] at (1,3)
\[y = x^3 at (1,1)\]

Answer 2

The derivative of the first equation is\[y \prime=4x ^{3}-18x ^{2}+26x-10\]At the point (0,5), the slope is -10.

Answer 3

The equation would use the point (0,5) to make:
y-5=-10(x-0)
y=-10x+5
So the normal line's equation would be y = 1/10x + 5

Answer 4

At the point (1,3), the slope of the tangent line is 2, and the equation would be
y-3=2(x-1)
y-3=2x-2
y=2x+1
So the equation for the normal line would be
y = -1/2x + 1

Answer 5

The last one has a derivative of \[y=3x ^{2}\]so at (1,1) the slope is 3. The equation would be
y-1=3(x-1)
y-1=3x-3
y=3x-2
So the equation for the normal line is
y=-1/3x-3

Answer 6

Are you with me on this?

Answer 7

I'm so sorry, hang on ill do this on paper

Answer 8

So we use (0, 5) with 0 for x and 5 for y?