SOLUTION: 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)

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)
Found 2 solutions by nerdybill, lwsshak3:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
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)

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
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)
..
f(x) = x^3 - 2x + 5
f'(x)=3x^2-2
f'(2)=12-2=10=m
f(2)=8-4+5=9
y=mx+b
using point (2,9)
9=10(2)+b
b=-11
Equation:
y=10x-11
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