Question

y=2x is a tangent to the curve y=x^3+ax+b at x=1. Find a and b.

Answer 1

Tangent line is the first derivative, so:

y' = 3x^2 + a;
x = 1; y' = 3*1^2 + a

Answer 2

3 + a = y'

Answer 3

now slope of ur tangent line is:
y= 2x; M = 2=> 3 + a = 2 => a = -1

Answer 4

but what the heck is b? lol im lost lemme see, kinda embarassing

Answer 5

wouldn't i just fill in a & fill in 1 for x to find b?

Answer 6

oh yeah, i think you do this:
you need y too when x=1, so
y = 2x = 2;
x = 1;
a = -1
2 = 1^3 + (-1)*1 + b
2 = 1 -1 +b => b = 2

Answer 7

can u check the answer?

Answer 8

yes that's right thank you so much!