SOLUTION: Hello, Please help me solve this. Stuck on it for 2 days and keep getting different answers. Question: Find the tangent to the curve y = 5x^3 + 2x -1 at x=2. I think y=43, deriv

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Question 768138: Hello,
Please help me solve this. Stuck on it for 2 days and keep getting different answers.
Question: Find the tangent to the curve y = 5x^3 + 2x -1 at x=2. I think y=43, derivative is 30 but really not sure now.
Thanks heaps.
Answer by Cromlix(4381) (Show Source):
You can put this solution on YOUR website!
Find the tangent to the curve y = 5x^3 + 2x -1 @ x = 2
y = 5x^3 + 2x -1
Differentiate
dy/dx = 15x^2 + 2
Put x = 2 into equation.
15x^2 + 2
15(2)^2 + 2
60 + 2
=62
This is the gradient of the tangent.
Now substitute x= 2 into your original
equation to find the y coordinate:
y = 5x^3 + 2x -1
y = 5(2)^3 + 2(2) - 1
y = 43
So these are the coordinates of
the point the tangent touches
the curve. (2,43)
Using equation:
y - b = m(x - a)
a = 2, b = 43 and m = 62
y - 43 = 62(x - 2)
y - 43 = 62x - 124
y = 62x - 124 + 43
y = 62x - 81
This the equation of the tangent.
Hope this helps.
:-)