Question

What is the slope ( M ) of the tangent to the curve y = 6 + 5² - 2x³ at the point where x = a, y(x) = at the point (1,9) and (2,10)?

a) M = -6

b) M = -12

c) M = 16

d) M = 12

Answer 1

The slope of the tangent line between the points (1, 9) and (2, 10) is 1, which does not match any of the provided answer choices, indicating an error in the question statement.

Step-by-step explanation:

The question given is asking about the slope of the tangent to a curve at a specific point where x equals a constant value 'a'. The curve is not provided, but points on a straight line segment are given as (1, 9) and (2, 10). To find the slope (m) of a line passing through these two points we use the slope formula: m = (y2 – y1) / (x2 – x1), where (x1, y1) and (x2, y2) are points on the line.

Plugging in our values we get:

m = (10 – 9) / (2 – 1)

m = 1 / 1

m = 1

However, this slope does not match any of the options given in the question, suggesting a possible typo or error in the problem statement. The additional irrelevant information provided does not contribute to solving this discrepancy.