# calculus

posted by .

please help! Find an equation of the tangent line to the curve at the point (-1, 1).
y = 5x3 - 6x.

• calculus -

Let f(x)=5x³-6x, then
f(-1)=5(-1)³-6(-1)=1
Slope at (x, f(x)) is given by dy/dx=f'(x)
f'(x) = dy/dx = 15x³-6
f'(-1)= 15(-1)²-6=9

Therefore you need a line with a slope of 9 to pass through the point (-1,1).
The standard equation for this is:

(y-y1)=m(x-x1)
where m=9, y1=-1, x1=1
(y-(-1)) = 9(x-1)
y=9x-9-1
y=9x-10 (slope of 9 and passes through (-1,1))

## Similar Questions

1. ### Calculus - Damon

Find the line which passes through the point (0, 1/4) and is tangent to the curve y=x^3 at some point. So I found the derivative which is 3x^2. Let (a, a3) be the point of tangency. 3x^2 = (a3 - 1/4)/(a-0) I'm not sure how to solve …
2. ### Calculus

Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean?
3. ### Calculus

Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean?
4. ### Calculus

Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean?
5. ### Calculus

Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean?
6. ### calculus

Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2 + 1 and connect the tangent point to the x-axis. If the tangent point is close to the y-axis, the line segment is long. If the tangent …
7. ### Calculus

Please help this is due tomorrow and I don't know how to Ive missed a lot of school sick Consider the curve given by the equation x^3+3xy^2+y^3=1 a.Find dy/dx b. Write an equation for the tangent line to the curve when x = 0. c. Write …
8. ### Tangent Lines-Calculus

a line is tangent to the curve y= (x^2 + 3)/ (x+3)^1/2 at the point where x=1. write the equation of this line i get y= 3x-1 yet it's wrong. please explain thank you
9. ### Calculus AB

Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x-1)e^x. For which value of x is the slope of the tangent line to f positive?