# What is the equation of the line tangent to # f(x)=(3x-1)(2x+4) # at # x=-1 #?

We can express the tangent line's equation in point-slope form as follows:

Forming the slope-intercept:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the equation of the line tangent to the function f(x)=(3x-1)(2x+4) at x=-1, we need to find the derivative of the function and evaluate it at x=-1.

First, let's find the derivative of f(x): f'(x) = (3x-1)(d/dx)(2x+4) + (2x+4)(d/dx)(3x-1) = (3x-1)(2) + (2x+4)(3) = 6x - 2 + 6x + 12 = 12x + 10

Next, let's evaluate the derivative at x=-1: f'(-1) = 12(-1) + 10 = -12 + 10 = -2

Now, we have the slope of the tangent line, which is -2. To find the equation of the line, we also need a point on the line. Since the line is tangent to the function at x=-1, we can use this point to find the y-intercept.

Using the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute the values: y - f(-1) = -2(x - (-1)) y - f(-1) = -2(x + 1) y - f(-1) = -2x - 2 y = -2x - 2 + f(-1)

Finally, we substitute f(-1) into the equation: y = -2x - 2 + f(-1) y = -2x - 2 + (3(-1)-1)(2(-1)+4) y = -2x - 2 + (-4)(2+4) y = -2x - 2 + (-4)(6) y = -2x - 2 - 24 y = -2x - 26

Therefore, the equation of the line tangent to f(x)=(3x-1)(2x+4) at x=-1 is y = -2x - 26.

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.

- How do you find the slope of a tangent line to the graph of the function# f(x)= -5/x^3# at x=6?
- How do you find the derivative of #(cos x)# using the limit definition?
- What is the first derivative of #x+ tanx# and how do you find the slope of the normal to the curve where #x=pi#?
- How do you find the slope of a tangent line to the graph of the function#2xy^2+xy=y# at y=1?
- How do you find the slope of the tangent line to the graph of the function #h(t)=t^2+3# at (-2,7)?

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