Can someone help me with this problem?

Question

Find the equation of the tangent line to the curve: f(x)=x^2,

a. Parallel to the line y = 8x + 2
b. Perpendicular to the line y = 8x + 2

Answer 1

slope of f(x) = 2x for any x.
Find where 2x = slope of desired line.

Now you have a point (x,y) and a slope.

Go for it.

Answer 2

slope = f'(x) = 2x

slope of y = 8x+2 is 8
2x=8
x=4, then y= 16
equation of tangent parallel is
y = 8x+b , at (4,16)
16 = 32+b
b = -16
y = 8x - 16

for perpendicular:
2x = -1/8
x = -1/16 , then y = 1/256
equation of perpendicular:
y = (-1/8)x+b
1/256 = -(1/8)x+b
1 = -65 + 256b
b = 66/256

y = (-1/8)x + 33/128

Answer 3

Thank you!!