How do you find the equation of the tangent line to the curve #y = (3x-1)(2x+4)# at the point of (0,-4)?

Answer 1

Use the product rule to compute the first derivative:

#dy/dx = (d(3x-1))/dx(2x+4) + (3x-1)(d(2x+4))/dx#
#dy/dx = 3(2x+4) + 2(3x-1)#
#dy/dx = 6x+12+6x-2#
#dy/dx= 12x+10#
The slope of the tangent line, m, is the first derivative evaluated at #x = 0#:
#m = 12(0)+10#
#m = 10#
Because the given point, #(0,-4)#, is the y intercept, one can use the slope-intercept form to write the equation of the tangent line:
#y = mx + b#
#y = 10x -4#
Sign up to view the whole answer

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

Sign up with email
Answer 2

To find the equation of the tangent line to the curve y = (3x-1)(2x+4) at the point (0,-4), we need to find the slope of the tangent line at that point.

First, we find the derivative of the function y = (3x-1)(2x+4) using the product rule.

The derivative is given by: y' = (3x-1)(2) + (2x+4)(3)

Simplifying this expression, we get: y' = 6x - 2 + 6x + 12

Combining like terms, we have: y' = 12x + 10

Now, we substitute x = 0 into the derivative to find the slope at the point (0,-4).

Substituting x = 0 into y', we get: y' = 12(0) + 10 = 10

Therefore, the slope of the tangent line at the point (0,-4) is 10.

Using the point-slope form of a linear equation, we can write the equation of the tangent line as:

y - y1 = m(x - x1)

Substituting the values of the point (0,-4) and the slope m = 10, we have:

y - (-4) = 10(x - 0)

Simplifying this equation, we get:

y + 4 = 10x

Rearranging the equation to the standard form, we have:

10x - y = -4

Therefore, the equation of the tangent line to the curve y = (3x-1)(2x+4) at the point (0,-4) is 10x - y = -4.

Sign up to view the whole answer

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

Sign up with email
Answer from HIX Tutor

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7