What is the equation of the normal line of #f(x)= x^3-3x^2-2x+6# at #x = 4#?
Equation of normal:
The line of normal will pass through the point From coordinate geometry, the gradient of the line of normal, The Equation of normal: Here is the graph
By signing up, you agree to our Terms of Service and Privacy Policy
To find the equation of the normal line at x = 4 for the function f(x) = x^3 - 3x^2 - 2x + 6, we need to determine the slope of the tangent line at x = 4 and then find the negative reciprocal of that slope to obtain the slope of the normal line.
To find the slope of the tangent line, we take the derivative of the function f(x) with respect to x.
The derivative of f(x) = x^3 - 3x^2 - 2x + 6 is f'(x) = 3x^2 - 6x - 2.
Evaluating f'(x) at x = 4, we get f'(4) = 3(4)^2 - 6(4) - 2 = 32.
The slope of the tangent line at x = 4 is 32.
To find the slope of the normal line, we take the negative reciprocal of the tangent line's slope.
The negative reciprocal of 32 is -1/32.
Therefore, the equation of the normal line at x = 4 is y - f(4) = (-1/32)(x - 4).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- How do you use the limit definition to find the derivative of #y = cscx#?
- What is the equation of the line tangent to #f(x)=(2x^3 - 4) / x# at #x=-4#?
- How do you find the instantaneous rate of change of revenue when 1000 units are produced if the revenue (in thousands of dollars) from producing x units of an item is #R(x) = 12x - .005x^2#?
- How do you find the points on the curve #y=x+2cosx# that have a horizontal tangent line?
- How do you find the equation of the tangent line #y=sinx# at #(pi/6, 1/2)#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7