Question 439367
Find the equation of the tangent line for the curve f(x) = x^3 - 2x + 5 at x = 2 (Write equation in y = mx + b form)
.
The problem gives you the 'x' at 2.
Find the 'y' by find the value of f(2):
f(2) = 2^3 - 2(2) + 5
f(2) = 8 - 4 + 5
f(2) = 9
'y' is 9
.
find the derivative:
f'(x) = 3x^2 - 2
f'(2) = 3(2)^2 - 2
f'(2) = 12 - 2
f'(2) = 10 (slope)
.
plug into "point-slope" form:
y - y1 = m(x - x1)
y - 9 = 10(x - 2)
y - 9 = 10x - 20
y = 10x - 11  (this is what they're looking for)