Question

Find the slope of the tangent line to the curve y = 3 + 4x^2 - 2x^3 at the point where x=a.

Answer 1

you need to differentiate that expression, which yeilds the slope of the curve at some arbitrary point a. and you have a point a, and 3 + 4a^2 - 2a^3, you have a point and a slope, thats all you need to define the line.

Answer 2

differentiate the curve

f'(x) = 8x - 6x^2 now find f'(a) to get the slope

Answer 3

gotta say i don't know what that means

Answer 4

wouldn't f'(a) be the same thing (8a - 6a^2)?

Answer 5

he found the derivative, and substituted x = a into it. so yes.