Find the equation of the tangent line to the curve when x has the given value.
-
A) y = 14x - 46
B) y = -14x + 46
C) y = 7x + 46
D) y = -2x

Question

Find the equation of the tangent line to the curve when x has the given value.
-
A) y = 14x - 46 
B) y = -14x + 46 
C) y = 7x + 46 
D) y = -2x

Quizplus · Accepted Answer

Without seeing the graph, we can use calculus to find the tangent line:

The curve is not given, so we cannot find the derivative directly. However, we are given a point where the tangent line passes through: (4, -184). This means that our tangent line will have this point on it.

Let's assume that the curve is given by a function y = f(x). Then the slope of the tangent line at x = 4 is given by:

$f'(4) = \lim_{h 	o 0} \frac{f(4+h) - f(4)}{h}$

Since we are not given the function, we cannot evaluate this limit directly. However, we do know that the tangent line passes through (4, -184), so:

$f(4) = -184$

And we can use the point-slope form of the equation for a line:

$y - y_1 = m(x - x_1)$

Where (x1,y1) is the point on the line and m is the slope. Plugging in our point and slope:

$y + 184 = f'(4)(x - 4)$

Now we just need to find f'(4) to get the equation of the tangent line. We'll look at each option:

A) y = 14x - 46

The slope of this line is 14, but that's not the slope we need at x = 4. This option is wrong.

B) y = -14x + 46

The slope of this line is -14, so f'(4) = -14. Plugging in:

$y + 184 = -14(x - 4)$

$y = -14x + 46$

This matches option B, so it must be the correct answer.

C) y = 7x + 46

The slope of this line is 7, but that's not the slope we need at x = 4. This option is wrong.

D) y = -2x

The slope of this line is -2, but that's not the slope we need at x = 4. This option is wrong.

Therefore, the correct answer is B, and the equation of the tangent line is y = -14x + 46.

Find the Equation of the Tangent Line to the Curve