# math

posted by .

4. For the curve with y = -2x3 + x - 6, find:

(b.) the gradient at the point (-1, -5)

(c.) the equation of the tangent line at the point (-1, -5).

• math -

y = -2x^3 + x - 6
dy/dx = -6x + 1

at (-1,-5), dy/dx = -6(-1) + 1 = 7

so y = -7x + b
at (-1,-5)
-5 = -7(-1) + b
b = -12

equation of tangent is y = -7x - 12

• math -

y = -2x^3 + x - 6
dy/dx = -6x + 1

at (-1,-5), dy/dx = -6(-1) + 1 = 7

so y = -7x + b
at (-1,-5)
-5 = -7(-1) + b
b = -12

equation of tangent is y = -7x - 12

## Similar Questions

1. ### Math

How can I determine a value of gradient from a graph if the line is curved. (not a straight line) This is where Calculus comes in If a graph is a curve, then the gradient (slope) of the curve is the slope of the tangent that you draw …
2. ### Calculus - Maths

I got a few questions. Hope ya'll can help out. 1) for F(X) = 6x - 2x^2 Find the gradient of the chord joining the point where the X coorinates are 1 and (1+h) respectively. b) hence find the gradient at x=1 2) Find the Coordinates …
3. ### math

With regards to question J: The variables x and y are connected by the equation y = x2 - x - 5. Some corresponding values of x and y are given in the table below. x -4 -3 -2 -1 0 1 2 3 4 5 y 15 7 a -3 -5 b -3 1 7 15 (a) Calculate the …
4. ### calculus

Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show that dy/dx= (4x-2xy)/(x^2+y^2+1) b. Write an equation of each horizontal tangent line to the curve. c. The line through the origin with slope -1 is tangent to the curve …
5. ### calculus

A curve passes through the point (1,-11) and it's gradient at any point is ax^2 + b, where a and b are constants. The tangent to the curve at the point (2,-16) is parallel to the x-axis. Find i) the values of a and b ii) the equation …
6. ### calculus

1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))?
7. ### calculus

1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))?
8. ### 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?