# How do you find the equation of the tangent line and normal line to the curve #y = (5+6x)^2# at the point (-4,361)?

- Equation of Tangent

Step1:

Step2:

Step3:

Equation of normal

The equation of normal is also a line of the same form as the tangent.

The only difference is at the level of the gradient.

We can deduce the gradient of the normal from the fact that the normal is a line perpendicular to the tangent

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To find the equation of the tangent line and normal line to the curve y = (5+6x)^2 at the point (-4,361), we need to find the derivative of the function at that point. The derivative of y = (5+6x)^2 is dy/dx = 12(5+6x).

To find the slope of the tangent line, substitute x = -4 into the derivative: dy/dx = 12(5+6(-4)) = -72.

The slope of the tangent line is -72.

To find the equation of the tangent line, use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point (-4,361).

Substituting the values, we have y - 361 = -72(x - (-4)). Simplifying, we get y = -72x + 23.

The equation of the tangent line is y = -72x + 23.

To find the slope of the normal line, we take the negative reciprocal of the slope of the tangent line. The negative reciprocal of -72 is 1/72.

To find the equation of the normal line, we use the point-slope form again: y - y1 = m(x - x1). Substituting the values, we have y - 361 = (1/72)(x - (-4)). Simplifying, we get y = (1/72)x + 361.

The equation of the normal line is y = (1/72)x + 361.

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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.

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