Question

what is the equation of the tangent line and of the normal line at the curve y = x^4 + 2e^x at the point (0,2) ?

Answer 1

find the derivative and plug in the point (0,2) that will be the slope for the tangent line.

Answer 2

next since you have a point you can use point slope form to find the tangent line
y-y1=m(x-x1)

where m is the slope( I already told you have to figure that out)
x1 and y1 is your point (0,2) = (x1,y1)

plug them in

Answer 3

if you wish to simplify then isolate y

Answer 4

no but what's the difference between the tangent line and the normal one!!!!

Answer 5

my textbook says the tangent line equation is y = 2x + 2 and the normal is y = (-1/2)(x) + 2

Answer 6

I got y = 2x + 2 as the tangent line by following the steps I showed you for finding the tangent line

Answer 7

The normal line is defined as the line that is perpendicular to the tangent line at the point of tangency.

Answer 8

which makes sense because perpendicular lines have an inverse of slope where the slope of the tangent line is 2
so inverse of 2 is -1/2