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spin [16.1K]
3 years ago
14

How to find (a) and (b)?​

Mathematics
1 answer:
rodikova [14]3 years ago
3 0

Answer:

A) Gradient = -3

B) 3y - x = 7

Step-by-step explanation:

The curve has the equation;

y = x³ - 6x² + 9x + 1

We are given the pints it passes through as;

A(2,3) and P(3, 1)

A) to find the gradient, we will find the derivative of the given equation.

Thus;

Gradient = y' = 3x² - 12x + 9

At point A, x = 2. Thus;

Gradient = 3(2²) - 12(2) + 9

Gradient = 12 - 24 + 9

Gradient = -3

B) since the gradient of the tangent = -3, it means the gradient of the normal will be; -1/-3 = 1/3

Thus, equation of the normal to the curve at point A will be;

(y - 3) = ⅓(x - 2)

Multiply both sides by 3 to get;

3y - 9 = x - 2

3y - x = 9 - 2

3y - x = 7

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Explanation:

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> This can be called "assigning one y-value to every x element".

The vertical line test places a line that would connect all y-values of an x-value (that is, if it were to have multiple y-values). If multiple points can be found along the vertical line, it is, therefore, by the definition of a function, not a function. (Because an x-value will have more than one y-value).

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hope this helps!!

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1 year ago
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8 0
1 year ago
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